OML Search

Factoring Difference of Squares

Related Topics:
More Lessons for Algebra
Math Worksheets

In some cases recognizing some common patterns in the trinomial or binomial will help you to factor it faster. For example, we could check whether the binomial is a difference of squares.

The following diagram gives examples of factoring difference of squares. Scroll down the page for more examples and solutions.

Difference of Squares

How to factor Difference of Squares?

A difference of squares is a binomial of the form:


Take note that the first term and the last term are both perfect squares.

When we factor a difference of two squares, we will get

a2b2 = (a + b)(a – b)

This is because (a + b)(a – b) = a2ab + ab – b2 = a2b2

x2 – 25 = 0
x2 – 52 = 0
(x + 5)(x – 5) = 0

We get two values for x: x + 5 ⇒ x = –5
x – 5 ⇒ x = 5

Be careful! This method only works for difference of two squares and not for the sum of two squares:
a2 + b2 ≠ (a + b)(ab)

Example :

a) x2– 9
b) 4x2– 25
c) 2x2– 32
d) πR2πr2


a) x2– 9
= x2– 32
= (x + 3)(x – 3)

b) 4x2– 25
= (2x)2– (5)2
= (2x + 5)(2x – 5)

c) 2x2– 32
= 2(x2– 16)
= 2(x2 – 42)
= 2(x + 4)(x – 4)

d) πR2πr2
= π(R2r2)
= π(R + r)(R – r)

The following videos explain how to factor a difference of squares.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.