Grade 9 · Math · Algebra 1

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

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Factor perfect squares and the difference of squares

Grade 9 Math Worksheet

NameDate

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

1.
Jun factors 4x² − 81 as a difference of squares. Which answer is right?
- (4x − 81)(4x + 81)
- (2x − 9)²
- (2x − 9)(2x + 9)
- (4x − 9)(4x + 9)
2.
Kira sees 9x² − 25 as one square minus another. Which is 9x² − 25 factored?
- (9x − 25)(9x + 25)
- (9x − 5)(9x + 5)
- (3x − 5)(3x + 5)
- (3x − 5)²
3.
Luz draws 16x² − 49 as a square with a corner cut out. Which is 16x² − 49 factored?
- (16x − 7)(16x + 7)
- (4x − 7)²
- (16x − 49)(16x + 49)
- (4x − 7)(4x + 7)
4.
Milo checks four answers for 49x² − 4. Which one is 49x² − 4 factored?
- (49x − 4)(49x + 4)
- (7x − 2)(7x + 2)
- (7x − 2)²
- (49x − 2)(49x + 2)
Noah wants 9x² + ▢x + 16 to be a perfect square with a plus sign. What number goes in the box?
Pia fills the gap so that 4x² + ▢x + 49 is a perfect square (plus sign). What number goes in the box?
7.
Zee sorts four trinomials into squares and not squares. Which one is a perfect square?
- 9x² − 42x − 49
- 9x² − 21x + 49
- 8x² − 42x + 49
- 9x² − 42x + 49
8.
Ari wants a trinomial that is a bracket squared. Which one is a perfect square?
- 16x² + 24x + 9
- 16x² + 24x − 9
- 16x² + 12x + 9
- 15x² + 24x + 9
9.
Bo has four tile patterns, and only one makes a square. Which trinomial is a perfect square?
- 25x² − 20x + 16
- 24x² − 40x + 16
- 25x² − 40x + 16
- 25x² − 40x − 16
10.
Esme checks four trinomials from a quiz. Which one is a perfect square?
- 4x² + 36x + 81
- 3x² + 36x + 81
- 4x² + 36x − 81
- 4x² + 18x + 81

9th grade Factor perfect squares and the difference of squares worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

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

What your child will learn

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

Words to know

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.

Common mistakes

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).

What to say

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?

Questions parents ask

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.

More algebra 1

See all Algebra 1

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