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−b2a^2 - b^2 into the product (a+b)(a−b)(a + b)(a - b).

When you multiply (a+b)(a−b)(a + b)(a - b), the middle terms cancel: a2−ab+ab−b2=a2−b2a^2 - ab + ab - b^2 = a^2 - b^2. 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 16x2−25y216x^2 - 25y^2.

Example 2

easy
Factor 16−y216 - y^2.

Example 3

medium
Use difference of squares to compute 532−47253^2 - 47^2 mentally.

Example 4

medium
Factor 50x2−850x^2 - 8.

Example 5

medium
Factor x2−14x^2 - \frac{1}{4}.

Example 6

challenge
Factor completely: a4−b4a^4 - b^4.

Example 7

medium
Factor 36x2−49y236x^2 - 49y^2.

Example 8

easy
Factor x2−100x^2 - 100.

Example 9

easy
Factor 1−49y21 - 49y^2.

Example 10

medium
Factor completely: 48−3y248 - 3y^2.

Example 11

challenge
Factor x4+x2+1x^4 + x^2 + 1 completely over the integers.

Example 12

easy
Factor x2−1x^2 - 1.

Example 13

easy
Factor x2−16x^2 - 16.

Example 14

medium
Factor 49a2−64b249a^2 - 64b^2.

Example 15

challenge
Factor x8−1x^8 - 1 completely over the reals.

Example 16

medium
Use difference of squares to compute 97×10397 \times 103.

Example 17

medium
Solve x2−49=0x^2 - 49 = 0 by factoring.

Example 18

easy
Factor 9x2−259x^2 - 25.

Example 19

hard
Factor x4−81x^4 - 81 completely.

Example 20

easy
Write 3636 as a perfect square: 36=?236 = ?^2.
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