Practice Distributive Property in Math

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

Quick Recap

The rule that multiplying a sum equals the sum of individual products: a(b+c)=ab+aca(b+c) = ab + ac. It links multiplication and addition, allowing you to break apart or combine terms.

Three packs of (2 red + 4 blue) = (3ร—23 \times 2 red) + (3ร—43 \times 4 blue) = 6 red + 12 blue.

Showing a random 20 of 59 problems.

Example 1

hard
Expand (x+1)(x2โˆ’x+1)(x + 1)(x^2 - x + 1).

Example 2

medium
Simplify 3(x+2y)โˆ’2(xโˆ’y)3(x + 2y) - 2(x - y).

Example 3

hard
A theater charges $12 per adult ticket and $8 per child ticket. A group buys aa adult and cc child tickets. Write a single expression and an equivalent expanded form for the total cost.

Example 4

medium
Show that 7ร—99=6937 \times 99 = 693 using the distributive property.

Example 5

medium
Expand (x+2)(x+3)(x + 2)(x + 3).

Example 6

medium
Jaden computes 4(10+3)4(10 + 3) like this: 4ร—10+3=434 \times 10 + 3 = 43. Find his mistake and enter the correct value.

Example 7

hard
Expand (x+y+z)2(x + y + z)^2.

Example 8

easy
Expand 6(yโˆ’4)6(y - 4).

Example 9

medium
Fill in the blank so the expansion is correct: 3(2x+__)=6x+213(2x + \_\_) = 6x + 21.

Example 10

medium
Factor completely: 12x+18yโˆ’2412x + 18y - 24.

Example 11

easy
Expand โˆ’(a+b)-(a + b).

Example 12

easy
Fill in the blank with the missing outside factor: __(x+3)=6x+18\_\_(x + 3) = 6x + 18.

Example 13

easy
Fill in the blank so the expansion is correct: 4(x+__)=4x+204(x + \_\_) = 4x + 20.

Example 14

medium
Now compute 2(10ร—4)2(10 \times 4). It looks almost like 2(10+4)2(10 + 4), but the symbol inside changed.

Example 15

easy
Factor 6x+96x + 9 by pulling out the common factor.

Example 16

easy
Expand 7(x+2)7(x + 2).

Example 17

easy
Factor 9xโˆ’129x - 12.

Example 18

easy
Use distribution to compute 6ร—126 \times 12 by splitting 12.

Example 19

easy
Fill in: 8(a+b)=8a+__8(a + b) = 8a + \_\_.

Example 20

medium
Expand โˆ’2(3aโˆ’4b+1)-2(3a - 4b + 1).