ALGEBRA

About "Algebra"

Algebra is a very important topic in mathematics. This topic is generally used for solving equations. 

Founders :

The major development of this topic was done in the ninth century by Arab mathematicians. In particular Al-Khwarzmi's book entitled "compendium on a  calculation by completing and balancing" was and significant event in the history of mathematics. So he is considered as the father of algebra.

In the sixth and seventh centuries, Indian mathematicians Aryabhatta and Brahmagupta have worked on the topics linear equations and quadratic equations and general method of solving.

In the 19th century British mathematicians took great effort on  developing this topic. The Peacock was the founder of axiomatic thinking in arithmetic. He is called as Euclid of algebra.

Topics of Polynomials

Terms factors and coefficients

Identify parts of an expression

Basic concept of polynomial

Like and unlike terms

How to combine like terms

Adding polynomials 

Subtracting polynomials

Multiplying polynomials

Multiply polynomial by a monomial

Multiplying binomials using FOIL method

Multiplying polynomials using box method

Dividing polynomials

Algebraic identities

Formula for (a + b)2

Formula for (a - b)2

Formula for a2 - b2

Formula for (x + a) (x + b)

Formula for (a + b)3

Formula for (a - b)3

Formula for a3 + b3

Formula for a3 - b3

Formula for (a + b + c)2

Applying the identities

Factorization

Factoring by grouping

Factoring polynomials using algebraic identities

Factoring quadratic equations

Solve quadratic equations by factoring

Factoring trinomials in box method

Factor out a monomial

Factor linear expressions

Factor polynomials

Finding prime factorization of a number

How to factor trinomial with 2 different variables

Solving Equations

Solving one step equations

Writing and solving one step inequalities

Solving one step equations word problems

Solving one step inequalities

Solving two step equations

Writing and solving two step inequalities

Solving two step equations with algebra tiles

Modeling and solving two step equations using algebra tiles

Solving quadratic equations

Solving equations using substitution

Solving equations using elimination

Solving equations using cross multiplication method

Solving equations in graphing method

Solving absolute value equations

Solving absolute value inequalities

Solving absolute value equations on both sides

Solving logarithmic equations

Square roots and squares

Radicals

Properties of radicals 

Operations with radicals

Solving radical equations with radicals on both sides

Simplify radical expressions

Comparison of surds

Squares 

Square roots of perfect square

Square roots of fractions and decimals

How to find square root of quadratic equation

How to find square root of polynomial

Finding square root by prime factorization method

Exponents and square roots

Estimating square roots

Other topics

L.C.M (least common multiple)

G.C.F(Greatest common factor)

Rational expression

Remainder theorem

Roots of cubic equation

Rationalize the denominator

Simplifying rational expression

Synthetic division

Framing quadratic equation from roots

Relationship between roots and coefficients

Partial fractions

Roots of polynomial of degree 4

Roots of polynomial of degree 5

After having gone through the stuff given above, we hope that the students would have understood this topic

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