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 - Challenge Me

NameDate

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

Jun races a calculator and wins. What is 53² − 47²?
Kira works out 38² − 32² with no calculator at all. What is 38² − 32²?
Milo beats a friend at mental math with 47² − 43². What is 47² − 43²?
4.
Noah factors 25x² − 36y², which has two letters. Which answer is right?
- (5x − 6y)²
- (5x − 6y)(5x + 6y)
- (25x − 36y)(25x + 36y)
- (25x − 6y)(25x + 6y)
5.
Pia sees two squares in 49x² − 9y². Which is 49x² − 9y² factored?
- (7x − 3y)(7x + 3y)
- (7x − 3y)²
- (49x − 3y)(49x + 3y)
- (49x − 9y)(49x + 9y)
6.
Ren draws 4x² − 121y² as a square with a square cut out. Which is 4x² − 121y² factored?
- (4x − 11y)(4x + 11y)
- (4x − 121y)(4x + 121y)
- (2x − 11y)(2x + 11y)
- (2x − 11y)²
7.
Tala checks four answers for 81x² − 16y². Which one is 81x² − 16y² factored?
- (81x − 16y)(81x + 16y)
- (9x − 4y)²
- (81x − 4y)(81x + 4y)
- (9x − 4y)(9x + 4y)
Zee cuts a 3-inch square from the corner of a square card x inches wide. The leftover x² − 9 becomes a rectangle. If x = 10, how long is its longer side?
Ari snips a 5-inch square off a square quilt patch x inches wide. The rest, x² − 25, is sewn into a rectangle. If x = 14, how long is its longer side?
Esme cuts a 9-inch square from a square poster board x inches wide. The rest, x² − 81, is rearranged into a rectangle. If x = 20, how long is its longer side?

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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