Grade 9 · Math · Algebra 1

9th grade Factor perfect squares and the difference of squares worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Factor perfect squares and the difference of squares

Grade 9 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

1.
Jun sorts four cards for a puzzle. Which binomial is a difference of squares?
- 6x² − 25
- x² + 49
- x² − 50
- x² − 225
2.
Luz finds four binomials in a workbook. Which is a difference of squares?
- x² − 27
- 3x² − 16
- x² − 169
- 4x² + 9
3.
Milo is choosing a binomial to factor at once. Which one is a difference of squares?
- x² + 36
- 8x² − 9
- x² − 72
- 4x² − 121
Noah cuts a small square out of a big square quilt patch. x² − 36 = (x − ▢)(x + ▢). What number goes in both boxes?
Ren sees x² − 361 as a square with a square cut out: (x − ▢)(x + ▢). What number goes in both boxes?
Tala factors x² − 324 = (x − ▢)(x + ▢) for a rug pattern. What number goes in both boxes?
Zee spots a perfect square: x² + 24x + 144 = (x + ▢)². What number goes in the box?
Ari builds a square from tiles: x² − 32x + 256 = (x − ▢)². What number goes in the box?
Bo checks a square on the board: x² − 28x + 196 = (x − ▢)². What number goes in the box?
Esme lays out a square rug pattern: x² + 40x + 400 = (x + ▢)². What number goes in the box?

Factor perfect squares and the difference of squares. Every version has 10 questions, and the answer key prints on the second page.

I can tell whether a binomial is a difference of squares.
I can factor a² − b² as (a − b)(a + b), and a perfect square trinomial as a bracket squared.
I can use a² − b² = (a − b)(a + b) to work out numbers like 53² − 47².

Standard: A-SSE.A.2

perfect square: A number or term that is something times itself, like 49 or 9x².

difference of squares: One square minus another, like x² − 64.

perfect square trinomial: Three terms that make a bracket squared, like x² + 24x + 144.

Your child picked a sum of two squares, like x² + 49, which cannot be factored with whole numbers.

Your child chose an expression with a part that is not a perfect square.

Your child used the squares themselves where the factors need their square roots (for example x − 64 instead of x − 8).

Ask: is there a minus sign between the two squares?

Ask: which number times itself gives this number?

Ask: which number times itself gives 64?

What is the most common mistake with factor perfect squares and the difference of squares?

Your child picked a sum of two squares, like x² + 49, which cannot be factored with whole numbers.

How can I help my child with factor perfect squares and the difference of squares?

Ask: is there a minus sign between the two squares?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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