Factor a difference of squares worksheets

x² − 64 is one square minus another, and it factors on sight into (x + 8)(x − 8). These free printable worksheets drill the plain difference of squares, no coefficient in front.

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Factor a difference of squares

The answer key prints on a separate page.

What's on this sheet

This is the one factorization with no search in it. There is no pair of numbers to hunt for and no middle term to match — the expression is one perfect square take away another, and it splits into the sum times the difference. What a child has to see is the shape: is each part a perfect square, and is the sign a minus.

Why this sheet works

The shape is exactly where the mistakes live. x² + 64 is a sum and does not factor at all, and x² − 20 is not a difference of squares because 20 is not a perfect square. A child who has learned the shortcut reaches for it on both; every walk here checks the two conditions before it factors anything.

How this one works

One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.

Factor a difference of squares, step by step

Difference of two squaresX² minus a square

Name: Date:

Each one is a difference of two squares. Factor it.

1x² − 64

2x² − 576

3x² − 625

4x² − 16

5x² − 25

6x² − 961

7x² − 1024

8x² − 100

9x² − 196

10x² − 9

Difference of two squares · X² minus a squareAnswer key

1. x² − 64 = (x + 8)(x − 8) (64 is 8 squared, so the two brackets are (x + 8) and (x − 8))2. x² − 576 = (x + 24)(x − 24) (576 is 24 squared, so the two brackets are (x + 24) and (x − 24))3. x² − 625 = (x + 25)(x − 25) (625 is 25 squared, so the two brackets are (x + 25) and (x − 25))4. x² − 16 = (x + 4)(x − 4) (16 is 4 squared, so the two brackets are (x + 4) and (x − 4))5. x² − 25 = (x + 5)(x − 5) (25 is 5 squared, so the two brackets are (x + 5) and (x − 5))6. x² − 961 = (x + 31)(x − 31) (961 is 31 squared, so the two brackets are (x + 31) and (x − 31))7. x² − 1024 = (x + 32)(x − 32) (1024 is 32 squared, so the two brackets are (x + 32) and (x − 32))8. x² − 100 = (x + 10)(x − 10) (100 is 10 squared, so the two brackets are (x + 10) and (x − 10))9. x² − 196 = (x + 14)(x − 14) (196 is 14 squared, so the two brackets are (x + 14) and (x − 14))10. x² − 9 = (x + 3)(x − 3) (9 is 3 squared, so the two brackets are (x + 3) and (x − 3))

Factor a difference of squares worksheets

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