Practice Factoring Difference of Squares in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Recognizing and factoring expressions of the form a2−b2 into the product (a+b)(a−b).

When you multiply (a+b)(a−b), the middle terms cancel: a2−ab+ab−b2=a2−b2. So any time you see a perfect square minus a perfect square, you can instantly factor it. Think of it as a rectangle whose area is the difference of two square areas.

Showing a random 20 of 50 problems.

Example 1

medium
Factor 16x2−25y2.

Example 2

easy
Factor 16−y2.

Example 3

medium
Use difference of squares to compute 532−472 mentally.

Example 4

medium
Factor 50x2−8.

Example 5

medium
Factor x2−14.

Example 6

challenge
Factor completely: a4−b4.

Example 7

medium
Factor 36x2−49y2.

Example 8

easy
Factor x2−100.

Example 9

easy
Factor 1−49y2.

Example 10

medium
Factor completely: 48−3y2.

Example 11

challenge
Factor x4+x2+1 completely over the integers.

Example 12

easy
Factor x2−1.

Example 13

easy
Factor x2−16.

Example 14

medium
Factor 49a2−64b2.

Example 15

challenge
Factor x8−1 completely over the reals.

Example 16

medium
Use difference of squares to compute 97×103.

Example 17

medium
Solve x2−49=0 by factoring.

Example 18

easy
Factor 9x2−25.

Example 19

hard
Factor x4−81 completely.

Example 20

easy
Write 36 as a perfect square: 36=?2.
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