The difference of the squares of any two quantities is equal to the product of their sum and difference, is called the difference of squares rule.

Let the literals $a$ and $b$ denote two variables.

- The addition of them forms a binomial $a+b$.
- The subtraction of them forms another binomial $a-b$.
- The difference of their squares also forms another binomial $a^2-b^2$.

According to a mathematical property, the difference of the squares of any two quantities is exactly equal to the product of their sum and difference. It can be written in mathematical form as follows.

$\implies$ $a^2-b^2$ $\,=\,$ $(a+b) \times (a-b)$

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

It is an algebraic identity and it is called the difference of squares law.

The difference of squares identity is also expressed in terms of variables $x$ and $y$ alternatively.

$x^2-y^2$ $\,=\,$ $(x+y)(x-y)$

The difference of squares algebraic identity is mainly used as a formula in two cases in mathematics.

- It is used to find the difference of squares of two quantities by calculating the product of sum and difference of the quantities.
- It is also used to convert the difference of squares of two quantities into the factor form for simplifying expressions and solving the equations.

List of the understandable examples to learn how to use the difference of squares rule in mathematics.

Latest Math Topics

Jul 24, 2022

Jul 15, 2022

Latest Math Problems

Sep 30, 2022

Jul 29, 2022

Jul 17, 2022

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

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

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

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved