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Multiplying Polynomials - Printable Mathematics Worksheets grade 9 - Wayground

Multiplying Polynomials

14 questions

9th - 12th Grade

Mathematics

Multiplying Polynomials is a free printable mathematics worksheet for students in Grades 9–12. It focuses on expanding products such as (x - 2)(x + 3), applying the distributive property to monomials and trinomials, multiplying powers of x, and simplifying polynomial expressions. Students answer 13 multiple-choice questions that progress from binomial products to expressions such as (x + 5)(x² + 3x + 5), with an additional open-ended class reflection prompt. The worksheet also includes a surface-area application in which students identify that the areas of separate rectangles must be added. It provides an opportunity to check whether students track coefficients, signs, exponents, and every term during multiplication. Use the included answer key to review the algebraic choices and discuss why distractors such as missing terms, incorrect exponents, or incomplete distribution are not equivalent expressions. The worksheet is available as a printable PDF with a complete answer key.

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Worksheets

Multiplying Polynomials

Total questions: 14

Name
Class
Date
1.

Select the expanded form of the expression:

(x - 2)(x + 3)

a)

(x + 1)

b)

(x - 6)

c)

(x + 6)

d)

(x2 + x + 1)

e)

(x2 + x - 6)

2.

Select the expanded form of the expression:

(x - 12)(x - 4)

a)

(x + 48)

b)

(x - 16)

c)

(x + 16)

d)

(x2 + x - 16)

e)

(x2 - 16x + 48)

3.

Select the expanded form of the expression:

(2x + 1)(x + 4)

a)

(x + 4)

b)

(x + 8)

c)

(x + 9)

d)

(x2 + 9x + 5)

e)

(2x2 + 9x + 4)

4.

Select the expanded form of the expression:

(2x + 1)(2x + 1)

a)

(2x + 2)

b)

(4x + 2)

c)

(4x + 4)

d)

(x2 + 8x + 2)

e)

(4x2 + 4x + 1)

5.

Select the expanded form of the expression:

(x2) (x3)

a)

x23

b)

x5

c)

x6

d)

x8

6.

2(x + 2)

a)

2x + 2

b)

2x + 4

c)

x2 + 2

d)

x2 + 4

7.

(x + 2)(x)

a)

2x + 2x

b)

2x + 4x

c)

x2 + 2x

d)

x2 + 4x

8.

(x)(x)

a)

2x

b)

x + 2

c)

x2

d)

x-2

9.

x(x2 + 3x + 5)

a)

x2 + 4x + 5

b)

x2 + 3x2 + 5x

c)

2x2 + 4x + 5x

d)

x3 + 3x2 + 5x

10.

5(x2 + 3x + 5)

a)

x5 + 8x + 10

b)

x2 + 3x + 10

c)

x2 + 3x + 10x

d)

5x3 + 15x2 + 5x

e)

5x2 + 15x + 25

11.

(x + 5) (x2 + 3x + 5)

a)

x2 + 4x + 10

b)

x3 + 8x2 + 20x + 25

c)

x3 + 3x2 + 5x + 5

12.

Mr. Mathews wants to redo the roof on the entire SFM building. To calculate the surface area of the roof, he breaks the building into multiple, varying size rectangles, and calculates the area for each rectangle.


In order to calculate the surface area of the roof, what must Mr. Mathews do with the areas of the individual rectangles?

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

13.

Overall, high school has been...

a)

Awesome!!

b)

Pretty good

c)

Just another school year

d)

Lonely

e)

Pretty Scary

14.

I like Mr. Sheldrake's class, but I think he should...

4 lines
Answer Key

Multiplying Polynomials

Total questions: 14

1.
e)

(x2 + x - 6)

2.
e)

(x2 - 16x + 48)

3.
e)

(2x2 + 9x + 4)

4.
e)

(4x2 + 4x + 1)

5.
b)

x5

6.
b)

2x + 4

7.
c)

x2 + 2x

8.
c)

x2

9.
d)

x3 + 3x2 + 5x

10.
e)

5x2 + 15x + 25

11.
b)

x3 + 8x2 + 20x + 25

12.
a)

Add

13.
n/a
14.
n/a

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FAQs

What does this multiplying polynomials worksheet help students practice?

This Grade 9–12 worksheet helps students expand and simplify polynomial products using the distributive property. Its mathematical questions include binomial multiplication, multiplying a monomial by a binomial or trinomial, applying exponent rules such as x² · x³ = x⁵, and recognizing that separate rectangle areas are added to find a total area. The 13 multiple-choice items include an open-ended class reflection prompt at the end.

How can I use this worksheet to teach multiplying polynomials?

Introduce the worksheet by modeling one binomial product with an area model or the FOIL method, then connect each partial product to a term in the expanded expression. Have students work through the simpler items, such as 2(x + 2) and (x)(x), before discussing the more complex trinomial product (x + 5)(x² + 3x + 5). Ask students to explain how they know all terms were distributed and combined, and use the roof-area question to connect adding partial areas with finding a total.

What mistakes should I watch for on this multiplying polynomials worksheet?

Watch for students dropping a term when multiplying binomials, mishandling negative signs in expressions such as (x - 12)(x - 4), or adding exponents incorrectly when multiplying powers of x. Students may also multiply only the first term of a trinomial by a coefficient, confuse x·x with 2x, or write x²·x³ as x⁶ instead of x⁵. In the surface-area item, check that they recognize the individual rectangle areas must be added rather than multiplied or divided.

How do I assign and grade this multiplying polynomials worksheet?

You can assign Multiplying Polynomials as a printable PDF or as a digital quiz on Wayground. The worksheet includes a complete answer key for the multiple-choice algebra and area questions; the open-ended class reflection requires teacher review. For printable submissions, scan student work with the Wayground for Teachers app to help grade responses.

How can I differentiate this multiplying polynomials worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing and font size to give students more room to write intermediate products or to make exponents and polynomial terms easier to read. You can also select a dyslexia-friendly font for the algebraic expressions or translate the worksheet into another language while keeping the multiplication tasks intact.

Where can I find more free worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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