Practice Distributive Property in Math

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

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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) = (3×23 \times 2 red) + (3×43 \times 4 blue) = 6 red + 12 blue.

Showing a random 20 of 50 problems.

Example 1

easy
Expand 5(a+2)5(a + 2).

Example 2

medium
Factor 7a+7b+7c7a + 7b + 7c.

Example 3

hard
Solve for xx: 4(x−1)+3(x+2)=5x+104(x - 1) + 3(x + 2) = 5x + 10.

Example 4

medium
Solve 5(2x+1)−3(x−4)=325(2x + 1) - 3(x - 4) = 32.

Example 5

medium
Simplify 3(x+2y)−2(x−y)3(x + 2y) - 2(x - y).

Example 6

easy
Factor 9x−129x - 12.

Example 7

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

Example 8

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

Example 9

medium
Solve 2(x+3)=162(x + 3) = 16.

Example 10

easy
Use distribution to compute 9×219 \times 21.

Example 11

medium
Expand (x+4)(x−3)(x + 4)(x - 3).

Example 12

easy
Expand 2(3x+5)2(3x + 5).

Example 13

medium
Simplify 2(x+1)+3(x+1)2(x + 1) + 3(x + 1) by factoring the common binomial.

Example 14

challenge
Factor x2+5xx^2 + 5x and then evaluate the factored form at x=7x = 7.

Example 15

easy
Expand 2(5x+3y)2(5x + 3y).

Example 16

medium
Expand and simplify 3(2x−5)+2(x+4)3(2x - 5) + 2(x + 4).

Example 17

medium
Expand and simplify 4(2x−3)−2(x−5)4(2x - 3) - 2(x - 5).

Example 18

medium
Expand −3(2x−5)-3(2x - 5).

Example 19

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 20

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