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Factoring by the Difference of squares

A method of factoring the difference of squares of two terms is called the factorization (or factorisation) by the difference of squares.

Introduction

A polynomial can be formed by the difference of two square quantities. It is not possible to subtract one term in square form from another term in square form due to the involvement of indeterminate variables. However, the subtraction of two square quantities is expressed in factor form.

Required knowledge

It is required to study the difference of squares rule to factorize (or factorise) the difference of two squares. The difference of squares rule is written popularly in the following two forms in mathematics.

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

Steps

Any expression in the form of difference of two squares can be factored easily by following below simple steps.

  1. Write each term of the expression in square form.
  2. Factorize the expression as a product of two binomials by using the difference of squares rule.

Example

Let’s learn how to factorise an expression by the difference of squares from the below example.

Factorize $16x^2-49y^2$

Write every term in square form

Write each term in square form to apply the difference of squares rule in factor form.

$=\,\,\,$ $4^2x^2-7^2y^2$

$=\,\,\,$ $(4x)^2-(7y)^2$

Factorize by the sum of squares rule

Take $a = 4x$ and $b = 7y$. Now, express the difference of the squares in factor form.

$=\,\,\,$ $(4x+7y)(4x-7y)$

Problems

List of the math questions with solutions to learn how to factorize the difference of squares by using the difference of squares formula.

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