Difference of Squares Worksheet

This difference of squares worksheet helps students recognize and factor expressions that match the pattern $a^2 - b^2$. The printable set includes 12 randomized questions and an answer key on page 2.

What is a Difference of Squares?

A difference of squares is an expression with two perfect square terms separated by subtraction. It follows the pattern:

$a^2 - b^2 = (a - b)(a + b)$

Recognizing this pattern makes factoring much faster.

How to Factor a Difference of Squares

1. Check that there are exactly two terms.
2. Make sure both terms are perfect squares.
3. Confirm that the operation is subtraction.
4. Rewrite using the pattern $(a - b)(a + b)$.

Example

Factor $x^2 - 16$

This is $x^2 - 4^2$.

So:

$x^2 - 16 = (x - 4)(x + 4)$

FAQ

Q: Does $a^2 + b^2$ factor the same way?
A: No. The sum of squares does not factor the same way over the real numbers.

Q: How do I know if something is a perfect square?
A: Look for terms like $x^2$, $9$, $16y^2$, or anything that can be written as a quantity squared.