Math Doubts

Factoring the Difference of squares

A method of factoring the difference of any two square expressions is called as factoring the difference of squares.

Introduction

In mathematics, two unlike expressions in square form are often involved in subtraction. It is not possible to subtract one expression from another due to unknown quantities. The difference of them can be factored mathematically and it is essential in some cases. So, let’s learn how to factor the difference of any two squares.

Required knowledge

You have to study the following mathematical concepts because we use them in factorization of the difference of two squares.

  1. Factorization by taking out the common factors
  2. Difference of squares formula

Steps

Let’s learn how to factorise the difference of two squares.

  1. Check the given expression to confirm whether the two terms in the expression contain a common factor. If they have a common factor, then factorize the expression by taking out the common factor. Otherwise, proceed to the next step.
  2. Use the difference of squares rule for factorizing the expression as a product of two special binomials.

Example

Factorize the Algebraic expression $4x^2z-9y^2z$

In this algebraic expression problem, $z$ is a factor, which is commonly appearing in both terms of the expression. So, it is confirmed that there is a common factor in both terms.

Now, take the common factor out from the expression according to the factorization by taking out the common factors.

$\implies$ $4x^2z-9y^2z$ $\,=\,$ $z[4x^2-9y^2]$

Now, express each term in square form and apply the difference of two squares formula.

$\implies$ $4x^2z-9y^2z$ $\,=\,$ $z[(2x)^2-(3y)^2]$

$\implies$ $4x^2z-9y^2z$ $\,=\,$ $z[(2x+3y)(2x-3y)]$

$\,\,\, \therefore \,\,\,\,\,\,$ $4x^2z-9y^2z$ $\,=\,$ $z(2x+3y)(2x-3y)$

Thus, the difference of two square expressions is factored mathematically in mathematics.

Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more