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+ac. It links multiplication and addition, allowing you to break apart or combine terms.

Three packs of (2 red + 4 blue) = (3×2 red) + (3×4 blue) = 6 red + 12 blue.

Showing a random 20 of 59 problems.

Example 1

hard
Expand (x+1)(x2−x+1).

Example 2

medium
Simplify 3(x+2y)−2(x−y).

Example 3

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

Example 4

medium
Show that 7×99=693 using the distributive property.

Example 5

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

Example 6

medium
Jaden computes 4(10+3) like this: 4×10+3=43. Find his mistake and enter the correct value.

Example 7

hard
Expand (x+y+z)2.

Example 8

easy
Expand 6(y−4).

Example 9

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

Example 10

medium
Factor completely: 12x+18y−24.

Example 11

easy
Expand −(a+b).

Example 12

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

Example 13

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

Example 14

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

Example 15

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

Example 16

easy
Expand 7(x+2).

Example 17

easy
Factor 9x−12.

Example 18

easy
Use distribution to compute 6×12 by splitting 12.

Example 19

easy
Fill in: 8(a+b)=8a+__.

Example 20

medium
Expand −2(3a−4b+1).