Multiplying polynomials worksheet

Distributing, then FOIL, then the two special cases worth recognising on sight: a parenthesis squared, and a sum times a difference.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Multiplying Polynomials Date Period Find each product. $- 6 (- 6 a + 9)$ $(- 5 r - 9) (- 2 r - 4)$ ${(3 p - 3)}^{2}$ $(7 n + 11) (7 n - 11)$ $(- 6 v + 2) (- 7 v^{2} - 7 v + 7)$ $- 8 (- 3 y - 3)$ $(- 3 n + 5) (3 n - 6)$ ${(- 7 y + 4)}^{2}$ $(9 y + 12) (9 y - 12)$ $(- y + 9) (7 y^{2} + 5 y + 2)$ $9 (- 4 n - 9)$ $(5 n - 3) (- 9 n - 1)$ ${(3 b - 6)}^{2}$ $(7 n + 10) (7 n - 10)$ $(- 5 m + 6) (9 m^{2} + 2 m + 2)$ $- 3 (- 7 k - 9)$ $(8 k - 2) (- 2 k + 2)$ ${(3 p + 2)}^{2}$ $(9 y + 11) (9 y - 11)$ $(- 2 a - 3) (- a^{2} + a - 9)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Multiplying Polynomials

Date Period

Find each product.

$- 6 (- 6 a + 9)$
$(- 5 r - 9) (- 2 r - 4)$
${(3 p - 3)}^{2}$
$(7 n + 11) (7 n - 11)$
$(- 6 v + 2) (- 7 v^{2} - 7 v + 7)$
$- 8 (- 3 y - 3)$
$(- 3 n + 5) (3 n - 6)$
${(- 7 y + 4)}^{2}$
$(9 y + 12) (9 y - 12)$
$(- y + 9) (7 y^{2} + 5 y + 2)$
$9 (- 4 n - 9)$
$(5 n - 3) (- 9 n - 1)$
${(3 b - 6)}^{2}$
$(7 n + 10) (7 n - 10)$
$(- 5 m + 6) (9 m^{2} + 2 m + 2)$
$- 3 (- 7 k - 9)$
$(8 k - 2) (- 2 k + 2)$
${(3 p + 2)}^{2}$
$(9 y + 11) (9 y - 11)$
$(- 2 a - 3) (- a^{2} + a - 9)$



Sigma Prep · sigmaprep.io/worksheets Name Multiplying PolynomialsAnswer keyVersion 1 Date Period Find each product. $- 6 (- 6 a + 9)$ $36 a - 54$ $(- 5 r - 9) (- 2 r - 4)$ $10 r^{2} + 38 r + 36$ ${(3 p - 3)}^{2}$ $9 p^{2} - 18 p + 9$ $(7 n + 11) (7 n - 11)$ $49 n^{2} - 121$ $(- 6 v + 2) (- 7 v^{2} - 7 v + 7)$ $42 v^{3} + 28 v^{2} - 56 v + 14$ $- 8 (- 3 y - 3)$ $24 y + 24$ $(- 3 n + 5) (3 n - 6)$ $- 9 n^{2} + 33 n - 30$ ${(- 7 y + 4)}^{2}$ $49 y^{2} - 56 y + 16$ $(9 y + 12) (9 y - 12)$ $81 y^{2} - 144$ $(- y + 9) (7 y^{2} + 5 y + 2)$ $- 7 y^{3} + 58 y^{2} + 43 y + 18$ $9 (- 4 n - 9)$ $- 36 n - 81$ $(5 n - 3) (- 9 n - 1)$ $- 45 n^{2} + 22 n + 3$ ${(3 b - 6)}^{2}$ $9 b^{2} - 36 b + 36$ $(7 n + 10) (7 n - 10)$ $49 n^{2} - 100$ $(- 5 m + 6) (9 m^{2} + 2 m + 2)$ $- 45 m^{3} + 44 m^{2} + 2 m + 12$ $- 3 (- 7 k - 9)$ $21 k + 27$ $(8 k - 2) (- 2 k + 2)$ $- 16 k^{2} + 20 k - 4$ ${(3 p + 2)}^{2}$ $9 p^{2} + 12 p + 4$ $(9 y + 11) (9 y - 11)$ $81 y^{2} - 121$ $(- 2 a - 3) (- a^{2} + a - 9)$ $2 a^{3} + a^{2} + 15 a + 27$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Multiplying PolynomialsAnswer keyVersion 1

Date Period

Find each product.

$- 6 (- 6 a + 9)$ $36 a - 54$
$(- 5 r - 9) (- 2 r - 4)$ $10 r^{2} + 38 r + 36$
${(3 p - 3)}^{2}$ $9 p^{2} - 18 p + 9$
$(7 n + 11) (7 n - 11)$ $49 n^{2} - 121$
$(- 6 v + 2) (- 7 v^{2} - 7 v + 7)$ $42 v^{3} + 28 v^{2} - 56 v + 14$
$- 8 (- 3 y - 3)$ $24 y + 24$
$(- 3 n + 5) (3 n - 6)$ $- 9 n^{2} + 33 n - 30$
${(- 7 y + 4)}^{2}$ $49 y^{2} - 56 y + 16$
$(9 y + 12) (9 y - 12)$ $81 y^{2} - 144$
$(- y + 9) (7 y^{2} + 5 y + 2)$ $- 7 y^{3} + 58 y^{2} + 43 y + 18$
$9 (- 4 n - 9)$ $- 36 n - 81$
$(5 n - 3) (- 9 n - 1)$ $- 45 n^{2} + 22 n + 3$
${(3 b - 6)}^{2}$ $9 b^{2} - 36 b + 36$
$(7 n + 10) (7 n - 10)$ $49 n^{2} - 100$
$(- 5 m + 6) (9 m^{2} + 2 m + 2)$ $- 45 m^{3} + 44 m^{2} + 2 m + 12$
$- 3 (- 7 k - 9)$ $21 k + 27$
$(8 k - 2) (- 2 k + 2)$ $- 16 k^{2} + 20 k - 4$
${(3 p + 2)}^{2}$ $9 p^{2} + 12 p + 4$
$(9 y + 11) (9 y - 11)$ $81 y^{2} - 121$
$(- 2 a - 3) (- a^{2} + a - 9)$ $2 a^{3} + a^{2} + 15 a + 27$

How to do these

$(x - 3) (6 x - 2)$

Every term in the first parenthesis times every term in the second.
6x² - 2x - 18x + 6.
Collect the two middle terms.

The answer is $6 x^{2} - 20 x + 6$ .

Where students go wrong

Squaring term by term. (4p - 1)² is not 16p² + 1: the middle term is there whether you write it or not, and it is -8p. Multiply the parenthesis by itself and it cannot go wrong.

Also called FOIL, expanding parentheses, binomial multiplication or special products.

What you can put on this worksheet

A single term outside: $6 (v + 5)$ → $6 v + 30$
Two binomials: $(5 v + 4) (3 v + 1)$ → $15 v^{2} + 17 v + 4$
A binomial squared: ${(5 v + 4)}^{2}$ → $25 v^{2} + 40 v + 16$
A sum times a difference: $(4 v + 7) (4 v - 7)$ → $16 v^{2} - 49$
A binomial times a trinomial: $(5 v + 4) (4 v^{2} + 3 v + 1)$ → $20 v^{3} + 31 v^{2} + 17 v + 4$

Questions about these worksheets

Yes. Every multiplying polynomials sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the multiplying polynomials questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 5: a single term outside, two binomials, a binomial squared, a sum times a difference and a binomial times a trinomial. Tick as many as you want and set how many of each, or let it spread them evenly.

Squaring term by term. (4p - 1)² is not 16p² + 1: the middle term is there whether you write it or not, and it is -8p. Multiply the parenthesis by itself and it cannot go wrong.

Multiplying polynomials worksheet

Select your difficulty

Multiplying Polynomials

Multiplying PolynomialsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these multiplying polynomials worksheets free?+

Do the multiplying polynomials worksheets come with an answer key?+

Are these multiplying polynomials worksheets printable?+

What grade are these multiplying polynomials worksheets for?+

Can I get a different version of the same multiplying polynomials worksheet?+

Is this a free alternative to Kuta Software for multiplying polynomials?+

Can I choose how hard the multiplying polynomials questions are?+

What kinds of question are on a multiplying polynomials worksheet?+

What do students get wrong with multiplying polynomials?+