Practice Polynomial Multiplication in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Multiplying polynomials by distributing every term in one polynomial to every term in the other, then combining like terms.

Each term in the first polynomial must 'shake hands' with every term in the second. For two binomials like (x+3)(x+5)(x + 3)(x + 5), the FOIL method (First, Outer, Inner, Last) organizes the four handshakes: xโ‹…x+xโ‹…5+3โ‹…x+3โ‹…5x \cdot x + x \cdot 5 + 3 \cdot x + 3 \cdot 5.

Showing a random 20 of 50 problems.

Example 1

medium
Multiply (x+2)(x2โˆ’3x+1)(x+2)(x^2-3x+1).

Example 2

easy
Multiply (x+1)(x+1)(x+1)(x+1).

Example 3

challenge
If (x+a)(x+b)=x2+11x+24(x + a)(x + b) = x^2 + 11x + 24, find a+ba + b and aโ‹…ba \cdot b.

Example 4

easy
Distribute โˆ’3x(2x2โˆ’x+4)-3x(2x^2 - x + 4).

Example 5

easy
Expand (2xโˆ’5)2(2x - 5)^2.

Example 6

hard
A box has length x+4x + 4, width x+1x + 1, and height xx. Express the volume as an expanded polynomial.

Example 7

medium
Multiply (x+3)(xโˆ’3)(x+1)(x+3)(x-3)(x+1).

Example 8

easy
Multiply (x+4)(x+3)(x + 4)(x + 3) using FOIL.

Example 9

medium
A square has side length x+5x + 5. Express its area as an expanded polynomial.

Example 10

challenge
Expand (x+2)3(x+2)^3 using polynomial multiplication.

Example 11

medium
Find the coefficient of xx in the expansion of (x+3)(xโˆ’5)(x + 3)(x - 5).

Example 12

medium
Find the constant term of (2xโˆ’3)(x+4)(xโˆ’1)(2x - 3)(x + 4)(x - 1).

Example 13

easy
Multiply 5x2โ‹…4x35x^2 \cdot 4x^3.

Example 14

challenge
Find the coefficient of x2x^2 in (x+1)(x+2)(x+3)(x+1)(x+2)(x+3).

Example 15

easy
Expand (x+6)2(x + 6)^2.

Example 16

easy
Expand (xโˆ’7)(x+7)(x - 7)(x + 7).

Example 17

medium
Multiply 4x2(3x3โˆ’2x+7)4x^2(3x^3 - 2x + 7).

Example 18

easy
Distribute 5(2xโˆ’3)5(2x - 3).

Example 19

easy
Multiply 3xโ‹…4x3x\cdot4x.

Example 20

easy
Distribute x(x+3)x(x+3).