Expanding Polynomials Using the Box Method - Math worksheet answers

Sep 30, 2026

Uploaded by Ezra

Practice set for expanding products of binomials/trinomials into polynomials using the box method. Includes 10 problems presented as factored expressions in x, followed by an answer key listing the expanded polynomial forms with coefficients and like-term organization. The material is formatted for step-by-step expansion, with each item showing the structure of the factors before multiplication and simplification into standard polynomial terms.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Expand each problem using the box method

Expanding Polynomials Using the Box Method Name: | Expand each problem using the box method.
1) (-4x2-1x+8)(2x2-8x) 2) (2x2-4x)(-7x2+3x+8)

3) (8x2-9x)(5x2-4x+6) 4) (-6x2-3x+8)(-6x2+8x)

5) (2x2-6x+5)(-5x2-4x) 6) (-3x2+8x)(-7x2+6x)

7) (7x2+8x+4)(7x2-5x+5) 8) (4x2+5x-3)(-4x2+3x+3)

9) (-8x2-3x+2)(-9x2+6x) 10) (-6x2-5x)(8x2+8x-6)
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10. | | | Answers | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1-10 | 90 | | 80 | 70 | | 60 | 50 | 40 | 30 | 20 | 10 | 0 | [Math](Math www.CommonCoreSheets.com 8)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 8)[ 8](Math www.CommonCoreSheets.com 8) Expanding Polynomials Using the Box Method Name: Answer Key | Expand each problem using the box method.
1) (-4x2-1x+8)(2x2-8x) 2) (2x2-4x)(-7x2+3x+8)
-4x2 -1x 8 2x2 -4x | | | | Answers
1. -8x4+30x3+24x2-64x 2. -14x4+34x3+4x2-32x 3. 40x4-77x3+84x2-54x 4. 36x4-30x3-72x2+64x 5. -10x4+22x3-x2-20x 6. 21x4-74x3+48x2 7. 49x4+21x3+23x2+20x+20 8. -16x4-8x3+39x2+6x-9 9. 72x4-21x3-36x2+12x 10. -48x4-88x3-4x2+30x | | --- | --- | --- | --- | --- | | 2x2
-8x | -8x4 -2x3 16x2 32x3 8x2 -64x | -7x2
3x 8 | -14x4 28x3 6x3 -12x2 16x2 -32x | | | 3) (8x2-9x)(5x2-4x+6) 4) (-6x2-3x+8)(-6x2+8x)
8x2 -9x -6x2 -3x 8
5x2
-4x 6
40x4 -45x3 -32x3 36x2 48x2 -54x
-6x2 8x
36x4 18x3 -48x2 -48x3 -24x2 64x
5) (2x2-6x+5)(-5x2-4x)
2x2 -6x 5
-5x2 -4x
-10x4 30x3 -25x2 -8x3 24x2 -20x
7) (7x2+8x+4)(7x2-5x+5)
7x2 8x 4
7x2
-5x 5
49x4 56x3 28x2 -35x3 -40x2 -20x 35x2 40x 20
9) (-8x2-3x+2)(-9x2+6x)
-8x2 -3x 2
-9x2 6x
72x4 27x3 -18x2 -48x3 -18x2 12x
6) (-3x2+8x)(-7x2+6x)
-3x2 8x
-7x2 6x
21x4 -56x3 -18x3 48x2
8) (4x2+5x-3)(-4x2+3x+3)
4x2 5x -3
-4x2
3x 3
-16x4 -20x3 12x2 12x3 15x2 -9x 12x2 15x -9
10) (-6x2-5x)(8x2+8x-6)
-6x2 -5x
8x2 8x-6
-48x4 -40x3 -48x3 -40x2 36x2 30x | | | | | [Math](Math www.CommonCoreSheets.com 8 1-10)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 8 1-10)[ 8](Math www.CommonCoreSheets.com 8 1-10)[ 1-10](Math www.CommonCoreSheets.com 8 1-10) 90 80 70 60 50 40 30 20 10 0 | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | Expanding Polynomials Using the Box Method Name: | Expand each problem using the box method. -8x 4 +30x 3 +24x 2-64x-14x4 +34x 3 +4x 2-32x 21x 4-74x 3 +48x 2 -10x 4 +22x 3-x 2-20x 40x 4-77x 3 +84x 2-54x 36x 4-30x 3-72x 2 +64x 1)
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5) (-4x2-1x+8)(2x2-8x) 2)

(8x2-9x)(5x2-4x+6) 4)

(2x2-6x+5)(-5x2-4x) 6)
(2x2-4x)(-7x2+3x+8)

(-6x2-3x+8)(-6x2+8x)

(-3x2+8x)(-7x2+6x)
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FAQs

How many problems are included in this worksheet?

There are 10 expansion problems in the set, labeled 1 through 10.

What method does the worksheet use to expand the expressions?

The worksheet instructs students to expand each problem using the box method.

Where can the expanded results be found?

An answer key provides the expanded polynomial forms for each numbered problem.

Sep 30, 2026

Uploaded by Ezra