Math Doubts

Algebraic identities

An equality property between two algebraic expressions is called an algebraic identity.

Introduction

In algebra, two expressions in algebraic form are equal. The mathematical relationship between them is called an algebraic identity. There are some useful algebraic identities and they are used as formulas in mathematics. The following is the list of algebraic formulae with proofs and understandable examples to learn how to use them mathematically.

Binomial identities

The list of standard algebraic identities to expand the binomials, which have exponents.

$(1). \,\,\,$ $(a+b)^2$ $\,=\,$ $a^2+b^2+2ab$

$(2). \,\,\,$ $(a-b)^2$ $\,=\,$ $a^2+b^2-2ab$

$(3). \,\,\,$ $(a+b)(a-b)$ $\,=\,$ $a^2-b^2$

$(4). \,\,\,$ $(a+b)^3$ $\,=\,$ $a^3+b^3+3ab(a+b)$

$(5). \,\,\,$ $(a-b)^3$ $\,=\,$ $a^3-b^3-3ab(a-b)$

Special Binomials Products

The list of standard algebraic identities to multiply some special form binomials.

$(1). \,\,\,$ $(x+a)(x+b)$ $\,=\,$ $x^2+(a+b)x+ab$

$(2). \,\,\,$ $(x+a)(x-b)$ $\,=\,$ $x^2+(a-b)x-ab$

$(3). \,\,\,$ $(x-a)(x+b)$ $\,=\,$ $x^2-(a-b)x-ab$

$(4). \,\,\,$ $(x-a)(x-b)$ $\,=\,$ $x^2-(a+b)x+ab$

Trinomial identities

The list of standard algebraic identities to expand the squares of trinomials.

$(1). \,\,\,$ ${(a+b+c)}^2$ $=$ $a^2$ $+$ $b^2$ $+$ $c^2$ $+$ $2ab$ $+$ $2bc$ $+$ $2ca$

$(2). \,\,\,$ ${(a+b-c)}^2$ $=$ $a^2$ $+$ $b^2$ $+$ $c^2$ $+$ $2ab$ $-$ $2bc$ $-$ $2ca$

$(3). \,\,\,$ ${(a-b+c)}^2$ $=$ $a^2$ $+$ $b^2$ $+$ $c^2$ $-$ $2ab$ $-$ $2bc$ $+$ $2ca$

$(4). \,\,\,$ ${(a-b-c)}^2$ $=$ $a^2$ $+$ $b^2$ $+$ $c^2$ $-$ $2ab$ $+$ $2bc$ $-$ $2ca$

Math Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved