EMTeachline algebra problem solving software - algebra tutorial

EMSolution Algebra short

EMTeachline Mathematics Software - interactive math problem solving, test authoring

Get an effective help in learning problem-solving skills and grasping math concepts! EMSolution offers an infinite number of fully explained solutions. Each solution evolves step by step; each step of solution is provided with its objective, grounding definition and rule and with underlying formula or theorem. EMSolution encourages students to learn through in-depth understanding of each solution step and repetition rather than through rote memorization. You can review solutions step by step, learn related math concepts, study solution methods, try to solve similar math problems on your own, and in parallel, learn math lexicon in a foreign language! For math teachers, EMSolution offers a number of easy-to-use test authoring options. You can select problems by topic, solution method and complexity level, prepare printable math tests and develop numerous test variants literally in a minute. A difficulty scale for each task will assist teachers in a class of mixed ability students. Free fully functional downloadable version of EMSolution is available. Free online demos allow trying most of the user options and viewing examples of fully explained solutions.

Parameters of the program

Name of program:	EMSolution_Algebra_short
Number of problems:	35126
Number of similar variants:	3
Languages of interface:	English, German
Price:	71 EUR
Size of archive:	4045 kb

35254 algebraic problems. Algebra 1 and Algebra 2 levels. Fully explained step-by-step solutions and proofs. Transformation, simplification and evaluation of rational expressions. Proofs of identities. Solutions of equations. Solutions of inequalities. Linear, quadratic, cubic, reciprocal, high-degree and fractional expressions. Related theory. Option of translation. Sorting problems by topics, complexity levels and solution methods. Authoring options enabling development of tests, quizzes, exams and problem solving lesson plans. Automatic generation of variant tests. Dozens of ready tests.

System Requirements:

Pentium 2 or higher

64 MB RAM

Windows 98 or higher

Internet Explorer 5.5 or higher

Plug-in MathPlayer (downloadable from here)

Program's detail

●	Examples
●	Press release
●	Contents of the program
●	Characteristics of similar programs

Examples

An online sample of math problems and problem solutions from this program is provided below:

●	Problems: Algebra

EMTEACHLINE MATHEMATICS SOFTWARE: MATH PROBLEM SOLVING FOR KIDS AND TEENS

Press release

ABSTRACT. EMTeachline Software has released a PC-based mathematics software package that offers a huge collection of problem-solving lessons in arithmetic, pre-algebra, algebra, trigonometry and hyperbolic trigonometry with hands-on tutorials. This encyclopedic software contains hundreds of thousands of fully explained step by step solutions to math problems from basic to advanced and thousands of related definitions, rules, math formulas and theorems. Each step of solution is provided with its objective, relevant definition and rule, and with fully explained step by step proof of the underlying math formulae or theorem. The software helps children review, explore and effectively learn essential math skills. Easy-to-use test authoring tools enable math teachers to develop customizable math tests, variant tests, quizzes, exams and problem-solving lesson plans. The software is suitable for elementary, middle and high school use. Designed as a supplement classroom instruction. Provides a useful help for math teachers.

1. SOFTWARE OVERVIEW

Building problem solving skills in math requires grasping math concepts and a large amount of training in solving similar tasks. EMTeachline Mathematics Software provides children with the chance to do just that. This software encourages kids to learn through in-depth understanding of each solution step and repetition rather than through rote memorization. Children who are struggling in math learn best through repetition. Those who stick with this mathematics software will come away with a stronger understanding of fundamental math concepts, improved higher-level thinking skills and excellent skills in solving math problems.

EMTeachline Mathematics Problem Solving Software - EMSolution - consists of dozens of modules arranged in topics. Each module offers hundreds of math problem types, with dozens of similar math problems within one type. Math learning is effective when problems gradually advance in difficulty. This software offers 11 levels of complexity for each problem type, from basic to extra difficult. Kids who are strong in math and need a challenge can adjust the difficulty level at any moment.

Learners can review solutions step by step and study related math theory. Each step of solution is provided with its objective, relevant definition and rule, and with fully explained step by step proof of the underlying math formulae or theorem. This tutoring material is provided in a useful manner, so that it is always under hand. A set of ready math tests is designed for children to review and reinforce their math skills. Problem situations, solutions and tutoring material can be printed out.

More than just a math tutorial, this bilingual problem-solving software offers a way for children to learn math lexicon in a foreign language. Translation of any text to German (or another language) is easily obtained by double-clicking on it. Those who study not in a native language will find this option particularly attractive.

Test authoring options make development of math tests, quizzes, homeworks and exams an easy and creative work. With thousands math problems at hands, math teachers do not have to search for fresh exmples. You can select math problems by complexity levels, solution methods and types of tasks; develop customizable math tests of varied complexity in a minute; create your own didactic materials and problem-solving lesson plans, and generate numerous similar variant tests around a constructed example. All developed materials can be printed out or stored in a file and re-used. These easy-to-use authoring tools provide an ideal solution for a classroom teacher.

Let's be honest -- this program is not for fun-seekers. No sounds, no colorful visual effects. The tutorial material is presented in a dry academic fashion. Most kids would use this program to review for an exam that they are required to take. However, the contents hold much appeal for children who enjoy solving math problems and like challenges. Those who look for a systematic math knowledge will find the software to be particularly engaging.

2. SKILLS COVERED

Arithmetic and Pre-Algebra: Operations: multiplication, division, addition, subtraction. Fractions, powers. Numeric expressions: estimation, equivalencies, problem-solving. Solving arithmetic problems using algebraic formulas.

Algebra: Polynomial and fractional rational expressions: transformation, simplification, evaluation. Solution of linear, quadratic, cubic, biquadratic, reciprocal and fractional algebraic equations and inequalities. Proofs of algebraic identities. Solution methods: Substitution, factoring, grouping, Bezout theorem, formulas of short multiplication, method of intervals and more. Related theory: definitions and rules, proof of algebraic formulas and theorems.

Trigonometry and Hyperbolic Trigonometry: trigonometric and hyperbolic functions, arcus functions. Trigonometric and hyperbolic expressions: transformation, simplification, evaluation. Solution of trigonometric and hyperbolic equations. Proofs of trigonometric and hyperbolic identities. Solution methods: universal substitution, sum, product and addition of trigonometric functions, power reduction, multiple argument, shift of argument and more. Related theory: definitions and rules, proof of trigonometric and hyperbolic formulas.

3. USER OPTIONS

For math students: You can review solutions of math problems step by step, learn related math concepts, study solution methods, review proofs of used math formulas, try to solve similar math problems on your own, and in parallel, learn math lexicon in a foreign language!

For math teachers: You can use an extensive bank of math problems; arrange problems by topic, complexity level, solution method and type of task; compile math tests, quizzes, homeworks and exams of varied complexity; create your own didactic materials and problem-solving lesson plans; generate numerous similar variant math tests around a constructed example. You can use dozens of ready variant tests.

Contents of the program

Themes

Rational expressions. Computational problems
Rational expressions. Transformations and proofs
Rational expressions. Proofs of inequalities
Rational equations
Rational inequalities

Chapters and sections

Rational expressions. Computational problems
Chapters	Sections
Evaluation of linear expressions and expressions reduced to them	Evaluation of linear expressions and expressions reduced to them. Elementary linear expressions. Evaluation Evaluation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions. Evaluation Evaluation of linear expressions and expressions reduced to them. Linear expressions. Distributive law. Evaluation Evaluation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Evaluation Evaluation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes. Evaluation Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers. Evaluation Evaluation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions. Evaluation Evaluation of linear expressions and expressions reduced to them. Fractional expressions reduced to linear expressions. Evaluation Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients. Evaluation Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients. Evaluation Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients. Evaluation Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients. Evaluation Evaluation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial. Evaluation Evaluation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law. Evaluation Evaluation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication. Evaluation Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law. Evaluation Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Formulas of short multiplication. Evaluation
Evaluation of quadratic expressions and expressions reduced to them	Evaluation of quadratic expressions and expressions reduced to them. Elementary quadratic expressions. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Distributive law. Integer coefficients. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Formulas of short multiplication. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Distributive law. Rational coefficients. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Factorization of quadratic trinomial. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Properties of powers. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Grouping method. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Distributive law. Integer coefficients. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Distributive law. Rational coefficients. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Integer coefficients. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Rational coefficients. Evaluation Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Factorization of quadratic trinomial. Evaluation
Evaluation of algebraic high-degree expressions	Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Bezout theorem. Integer roots. Evaluation Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Bezout theorem. Irrational roots. Evaluation Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Bezout theorem. Integer roots. Evaluation Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Grouping method. Evaluation Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Perfect square. Evaluation Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Bezout theorem. Irrational roots. Evaluation Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Formulas of short multiplication. Evaluation Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Difference of squares. Evaluation Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Factorization of quadratic trinomial. Evaluation Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Properties of fractions. Evaluation Evaluation of algebraic high-degree expressions. Algebraic high-degree expressions. Difference and sum of cubes. Evaluation
Evaluation of fractional algebraic expressions	Evaluation of fractional algebraic expressions. Elementary fractional algebraic expressions. Evaluation Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator. Evaluation Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator. Evaluation Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator. Evaluation Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator. Evaluation Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Evaluation
Comparison of values of linear expressions and expressions reduced to them	Comparison of values of linear expressions and expressions reduced to them. Elementary linear inequalities Comparison of values of linear expressions and expressions reduced to them. Elementary linear inequalities containing fractions Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Distributive law Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication. Cubes. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Properties of powers. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Inequalities reduced to linear inequalities. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Rational coefficients. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Integer coefficients. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Integer coefficients. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Rational coefficients. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Factorization of quadratic trinomial. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Distributive law. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Formulas of short multiplication. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Properties of fractions. Distributive law. Comparison of values Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Properties of fractions. Formulas of short multiplication. Comparison of values
Comparison of values of quadratic expressions and expressions reduced to them	Comparison of values of quadratic expressions and expressions reduced to them. Elementary quadratic expressions. Comparison Comparison of values of quadratic expressions and expressions reduced to them. Compare quadratic expressions containing fractions Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Distributive law. Integer coefficients Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Formulas of short multiplication Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Distributive law. Rational coefficients Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Factorization of quadratic trinomial Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Properties of powers Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Grouping method Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Distributive law. Integer coefficients Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Distributive law. Rational coefficients Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Integer coefficients Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Rational coefficients Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Factorization of quadratic trinomial
Comparison of values of algebraic high-degree expressions	Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Bezout theorem. Irrational roots Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Bezout theorem. Integer roots Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Grouping method Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Perfect square Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Formulas of short multiplication Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Difference of squares Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Factorization of quadratic trinomial Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Properties of fractions Comparison of values of algebraic high-degree expressions. Compare algebraic high-degree expressions. Difference and sum of cubes
Comparison of values of fractional algebraic expressions	Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with linear expression in numerator Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with quadratic expression in numerator Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with cubic expression in numerator Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator

Rational expressions. Transformations and proofs
Chapters	Sections
Transformation of linear expressions and expressions reduced to them	Transformation of linear expressions and expressions reduced to them. Elementary linear expressions Transformation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Transformation of linear expressions and expressions reduced to them. Linear expressions. Distributive law Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Transformation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers Transformation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Transformation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
Transformation of quadratic algebraic expressions and expressions reduced to them	Transformation of quadratic algebraic expressions and expressions reduced to them. Elementary quadratic expressions Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions containing fractions Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Decomposition of quadratic trinomial Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Grouping method Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Factorization of quadratic trinomial Transformation of quadratic algebraic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Integer coefficients
Transformation of algebraic high-degree expressions	Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Irrational roots Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots Transformation of algebraic high-degree expressions. High degrees. Grouping method Transformation of algebraic high-degree expressions. High degrees. Perfect square Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots Transformation of algebraic high-degree expressions. High degrees. Formulas of short multiplication Transformation of algebraic high-degree expressions. High degrees. Difference of squares Transformation of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial Transformation of algebraic high-degree expressions. High degrees. Properties of fractions Transformation of algebraic high-degree expressions. High degrees. Difference and sum of cubes
Transformation of fractional algebraic expressions	Transformation of fractional algebraic expressions. Elementary fractional algebraic expressions Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution
Factorization of linear expressions and expressions reduced to them	Factorization of linear expressions and expressions reduced to them. Elementary linear expressions Factorization of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Factorization of linear expressions and expressions reduced to them. Linear expressions. Distributive law Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Factorization of linear expressions and expressions reduced to them. Linear expressions. Properties of powers Factorization of linear expressions and expressions reduced to them. Expressions reduced to linear expressions Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Factorization of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
Factorization of quadratic expressions and expressions reduced to them	Factorization of quadratic expressions and expressions reduced to them. Elementary quadratic expressions Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
Factorization of algebraic high-degree expressions	Factorization of algebraic high-degree expressions. High degrees. Grouping method Factorization of algebraic high-degree expressions. High degrees. Perfect square Factorization of algebraic high-degree expressions. High degrees. Formulas of short multiplication Factorization of algebraic high-degree expressions. High degrees. Difference of squares Factorization of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial Factorization of algebraic high-degree expressions. High degrees. Properties of fractions Factorization of algebraic high-degree expressions. High degrees. Difference and sum of cubes
Proof of identity. Linear expressions and expressions reduced to them	Proof of identity. Linear expressions and expressions reduced to them. Elementary linear expressions Proof of identity. Linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Distributive law Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Properties of powers Proof of identity. Linear expressions and expressions reduced to them. Expressions reduced to linear expressions Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law
Proof of identity. Quadratic expressions and expressions reduced to them	Proof of identity. Quadratic expressions and expressions reduced to them. Elementary quadratic expressions Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Grouping method Proof of identity. Quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Integer coefficients Proof of identity. Quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Rational coefficients
Proof of identity. High-degree expressions	Proof of identity. High-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots Proof of identity. High-degree expressions. High degrees. Bezout theorem. Irrational roots Proof of identity. High-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots Proof of identity. High-degree expressions. High degrees. Grouping method Proof of identity. High-degree expressions. High degrees. Perfect square Proof of identity. High-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots Proof of identity. High-degree expressions. High degrees. Formulas of short multiplication Proof of identity. High-degree expressions. High degrees. Difference of squares Proof of identity. High-degree expressions. High degrees. Properties of fractions
Proof of identity. Fractional algebraic expressions	Proof of identity. Fractional algebraic expressions. Elementary fractional algebraic expressions Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator

Rational expressions. Proofs of inequalities
Chapters	Sections
Proof of strict inequalities. Linear expressions and expressions reduced to them	Proof of strict inequalities. Linear expressions and expressions reduced to them. Elementary linear inequalities Proof of strict inequalities. Linear expressions and expressions reduced to them. Elementary linear inequalities containing fractions Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Distributive law Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication. Cubes Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Properties of powers Proof of strict inequalities. Linear expressions and expressions reduced to them. Inequalities reduced to linear inequalities Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Rational coefficients Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Integer coefficients Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Integer coefficients Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Rational coefficients Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Factorization of quadratic trinomial Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Distributive law Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Formulas of short multiplication Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Properties of powers
Proof of strict inequalities. Quadratic expressions	Proof of strict inequalities. Quadratic expressions. Elementary quadratic inequalities Proof of strict inequalities. Quadratic expressions. Quadratic inequalities containing fractions Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Distributive law. Integer coefficients Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Grouping method Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Distributive law. Integer coefficients Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Distributive law. Rational coefficients Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Grouping method Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Factorization of quadratic trinomial Proof of strict inequalities. Quadratic expressions. Fractional inequalities. Method of substitution. Distributive law. Integer coefficients
Proof of strict inequalities. Algebraic high-degree expressions	Proof of strict inequalities. Algebraic high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots Proof of strict inequalities. Algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems
Proof of strict inequalities. Fractional algebraic expressions	Proof of strict inequalities. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator. To prove inequality Proof of strict inequalities. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator. To prove inequality

Rational equations
Chapters	Sections
Linear equations	Linear equations. Elementary linear equations Linear equations. Linear equations containing fractions Linear equations. Linear equations. Distributive law Linear equations. Equations reduced to linear equations. Formulas of short multiplication Linear equations. Linear equations. Formulas of short multiplication. Cubes Linear equations. Linear equations. Properties of powers Linear equations. Equations reduced to linear equations Linear equations. Homographic equations with rational coefficients. Properties of fractions Linear equations. Homographic equations with integer coefficients. Properties of fractions Linear equations. Homographic equations with integer coefficients. Method of substitution Linear equations. Homographic equations with rational coefficients. Method of substitution Linear equations. Linear equations. Factorization of quadratic trinomial Linear equations. Equations reduced to linear. Method of substitution. Distributive law Linear equations. Equations reduced to linear. Method of substitution. Distributive law. Formulas of short multiplication
Quadratic equations	Quadratic equations. Elementary quadratic equations Quadratic equations. Quadratic equations containing fractions Quadratic equations. Equations with integer coefficients. Distributive law Quadratic equations. Quadratic equations. Formulas of short multiplication Quadratic equations. Quadratic equations with rational coefficients. Distributive law Quadratic equations. Equations reduced to quadratic. Factorization of quadratic trinomial Quadratic equations. Equations reduced to quadratic. Properties of powers Quadratic equations. Fractional algebraic equations reduced to quadratic equations. Distributive law Quadratic equations. Equations. Grouping method Quadratic equations. Equations. Method of substitution. Distributive law. Integer coefficients Quadratic equations. Equations. Method of substitution. Distributive law. Rational coefficients Quadratic equations. Equations. Method of substitution. Formulas of short multiplication Quadratic equations. Equations. Method of substitution. Properties of fractions Quadratic equations. Equations. Method of substitution. Grouping method Quadratic equations. Equations. Method of substitution. Factorization of quadratic trinomial Quadratic equations. Fractional equations. Method of substitution. Distributive law Quadratic equations. Fractional equations reduced to quadratic equations. Method of substitution Quadratic equations. Fractional equations. Method of substitution. Formulas of short multiplication Quadratic equations. Fractional algebraic equations reduced to quadratic equations. Formulas of short multiplication
Cubic equations	Cubic equations. Cubic equations in reduced form Cubic equations. Cubic equations in general form
Algebraic equations. Method of substitution	Algebraic equations. Method of substitution. Elementary biquadratic equations Algebraic equations. Method of substitution. Algebraic equations reduced to biquadratic equations Algebraic equations. Method of substitution. Algebraic equations. Linear substitution Algebraic equations. Method of substitution. Algebraic equations. Quadratic substitution Algebraic equations. Method of substitution. Algebraic equations. Homographic substitution Algebraic equations. Method of substitution. Reciprocal equations Algebraic equations. Method of substitution. Algebraic equations reduced to reciprocal
Algebraic high-degree equations	Algebraic high-degree equations. High-degree equations. Bezout theorem. Integer roots Algebraic high-degree equations. High-degree equations. Bezout theorem. Irrational roots Algebraic high-degree equations. High-degree equations reduced to the form allowing application of the Bezout theorem. Integer roots Algebraic high-degree equations. High-degree equations. Grouping method Algebraic high-degree equations. High-degree equations. Perfect square Algebraic high-degree equations. High-degree equations reduced to the form allowing application of the Bezout theorem. Irrational roots Algebraic high-degree equations. High-degree equations. Formulas of short multiplication Algebraic high-degree equations. High-degree equations. Difference of squares Algebraic high-degree equations. High-degree equations. Factorization of quadratic trinomial Algebraic high-degree equations. High-degree equations. Properties of fractions Algebraic high-degree equations. High-degree equations. Difference and sum of cubes Algebraic high-degree equations. High-degree equations. Method of substitution
Fractional algebraic equations	Fractional algebraic equations. Elementary fractional algebraic equations Fractional algebraic equations. Fractional algebraic equations reduced to linear equations Fractional algebraic equations. Fractional algebraic equations reduced to quadratic equations Fractional algebraic equations. Fractional algebraic equations reduced to cubic equations Fractional algebraic equations. Fractional algebraic equations reduced to biquadratic equations Fractional algebraic equations. Fractional algebraic equations reduced to reciprocal equations Fractional algebraic equations. Fractional algebraic equations reduced to quadratic equations. Method of substitution Fractional algebraic equations. Fractional algebraic equations. Method of substitution

Rational inequalities
Chapters	Sections
Weak linear inequalities	Weak linear inequalities. Elementary linear weak inequalities Weak linear inequalities. Linear weak inequalities containing fractions Weak linear inequalities. Homographic weak inequalities. Method of substitution. Rational coefficients Weak linear inequalities. Linear weak inequalities. Distributive law Weak linear inequalities. Weak inequalities reduced to linear inequalities. Formulas of short multiplication Weak linear inequalities. Linear weak inequalities. Formulas of short multiplication. Cubes Weak linear inequalities. Linear weak inequalities. Properties of fractions Weak linear inequalities. Linear weak inequalities. Factorization of quadratic trinomial Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Distributive law Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Formulas of short multiplication Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Properties of powers Weak linear inequalities. Linear weak inequalities. Properties of powers Weak linear inequalities. Weak inequalities reduced to linear inequalities Weak linear inequalities. Fractional weak inequalities reduced to linear inequalities Weak linear inequalities. Homographic weak inequalities. Properties of fractions. Rational coefficients Weak linear inequalities. Homographic weak inequalities. Properties of fractions. Integer coefficients Weak linear inequalities. Homographic weak inequalities. Method of substitution. Integer coefficients Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Factorization of quadratic trinomial Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Distributive law Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Formulas of short multiplication Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Properties of powers Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Factorization of quadratic trinomial
Strict linear inequalities	Strict linear inequalities. Elementary strict linear inequalities Strict linear inequalities. Strict linear inequalities containing fractions Strict linear inequalities. Strict linear inequalities. Distributive law Strict linear inequalities. Strict inequalities reduced to linear inequalities. Formulas of short multiplication Strict linear inequalities. Strict inequalities reduced to linear inequalities. Formulas of short multiplication. Cubes Strict linear inequalities. Strict linear inequalities. Properties of fractions Strict linear inequalities. Strict linear inequalities. Properties of powers Strict linear inequalities. Strict inequalities reduced to linear inequalities Strict linear inequalities. Strict fractional inequalities reduced to linear inequalities Strict linear inequalities. Strict homographic inequalities. Properties of fractions. Rational coefficients Strict linear inequalities. Strict homographic inequalities. Properties of fractions. Integer coefficients Strict linear inequalities. Strict homographic inequalities. Method of substitution. Integer coefficients Strict linear inequalities. Strict homographic inequalities. Method of substitution. Rational coefficients Strict linear inequalities. Strict linear inequalities. Factorization of quadratic trinomial Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Distributive law Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Formulas of short multiplication Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Properties of powers Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Factorization of quadratic trinomial Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Distributive law Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Formulas of short multiplication Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Properties of powers Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Factorization of quadratic trinomial
Strict quadratic inequalities	Strict quadratic inequalities. Elementary quadratic strict inequalities Strict quadratic inequalities. Quadratic strict inequalities containing fractions Strict quadratic inequalities. Strict inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients Strict quadratic inequalities. Strict inequalities. Method of substitution. Distributive law. Rational coefficients Strict quadratic inequalities. Strict inequalities. Distributive law. Integer coefficients Strict quadratic inequalities. Strict inequalities. Formulas of short multiplication Strict quadratic inequalities. Strict inequalities. Distributive law. Rational coefficients Strict quadratic inequalities. Strict inequalities. Factorization of quadratic trinomial Strict quadratic inequalities. Strict inequalities. Properties of powers Strict quadratic inequalities. Fractional strict algebraic inequalities reduced to quadratic inequalities Strict quadratic inequalities. Strict inequalities. Grouping method Strict quadratic inequalities. Strict inequalities. Method of substitution. Distributive law. Integer coefficients Strict quadratic inequalities. Strict inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Distributive law. Integer coefficients Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Distributive law. Rational coefficients Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients
Weak quadratic inequalities	Weak quadratic inequalities. Elementary quadratic weak inequalities Weak quadratic inequalities. Quadratic weak inequalities containing fractions Weak quadratic inequalities. Weak inequalities. Distributive law. Integer coefficients Weak quadratic inequalities. Weak inequalities. Formulas of short multiplication Weak quadratic inequalities. Weak inequalities. Distributive law. Rational coefficients Weak quadratic inequalities. Weak inequalities. Factorization of quadratic trinomial Weak quadratic inequalities. Weak inequalities. Properties of powers Weak quadratic inequalities. Fractional algebraic weak inequalities reduced to quadratic inequalities Weak quadratic inequalities. Weak inequalities. Grouping method Weak quadratic inequalities. Weak inequalities. Method of substitution. Distributive law. Integer coefficients Weak quadratic inequalities. Weak inequalities. Method of substitution. Distributive law. Rational coefficients Weak quadratic inequalities. Weak inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients Weak quadratic inequalities. Weak inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Distributive law. Integer coefficients Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Distributive law. Rational coefficients Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients
Strict algebraic high-degree inequalities	Strict algebraic high-degree inequalities. Strict high-degree inequalities. Bezout theorem. Integer roots Strict algebraic high-degree inequalities. Strict high-degree inequalities. Bezout theorem. Irrational roots Strict algebraic high-degree inequalities. Strict high-degree inequalities. Bezout theorem. Integer roots Strict algebraic high-degree inequalities. Strict high-degree inequalities. Grouping method Strict algebraic high-degree inequalities. Strict high-degree inequalities. Perfect square Strict algebraic high-degree inequalities. Strict inequalities. Formulas of short multiplication Strict algebraic high-degree inequalities. Strict inequalities. Difference of squares Strict algebraic high-degree inequalities. Strict inequalities. Factorization of quadratic trinomial Strict algebraic high-degree inequalities. Strict inequalities. Properties of fractions Strict algebraic high-degree inequalities. Strict inequalities. Difference and sum of cubes
Weak algebraic high-degree inequalities	Weak algebraic high-degree inequalities. Weak high-degree inequalities. Bezout theorem. Integer roots Weak algebraic high-degree inequalities. Weak high-degree inequalities. Bezout theorem. Irrational roots Weak algebraic high-degree inequalities. Weak high-degree inequalities. Bezout theorem. Integer roots Weak algebraic high-degree inequalities. Weak high-degree inequalities. Grouping method Weak algebraic high-degree inequalities. Weak high-degree inequalities. Perfect square Weak algebraic high-degree inequalities. Weak inequalities. Formula of difference of squares Weak algebraic high-degree inequalities. Weak inequalities. Factorization of quadratic trinomial Weak algebraic high-degree inequalities. Weak inequalities. Properties of fractions Weak algebraic high-degree inequalities. Weak inequalities. Difference and sum of cubes
Strict fractional inequalities	Strict fractional inequalities. Elementary fractional strict algebraic inequalities Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict linear inequalities Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict quadratic inequalities Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict quadratic inequalities. Method of substitution
Weak fractional inequalities	Weak fractional inequalities. Elementary fractional weak algebraic inequalities Weak fractional inequalities. Fractional weak algebraic inequalities reduced to linear inequalities Weak fractional inequalities. Fractional weak algebraic inequalities reduced to quadratic inequalities Weak fractional inequalities. Fractional weak algebraic inequalities reduced to quadratic inequalities. Method of substitution

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