Pre-Algebra

Distributive Property

Lesson

The distributive propertysays that multiplication spreads (“distributes”) across addition or subtraction inside parentheses:

a(b + c) = ab + ac

a(b - c) = ab - ac

You multiply the outside factor by each term inside, then add or subtract the results.

Worked example 1

3(x + 4)

Multiply 3 by each term inside:

= 3 \cdot x + 3 \cdot 4

= 3x + 12

Worked example 2

-2(y - 5)

Be careful with the negative sign — it travels with the 2:

= -2 \cdot y + (-2) \cdot (-5)

= -2y + 10

How to type your answer

Variable term first, then the constant. No spaces needed. Examples: 3x+12, -2y+10, 5a-15.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

2(x + 1)

Problem 2

3(y + 5)

Problem 3

4(a + 2)

Problem 4

5(x - 1)

Practice

Standard problems matching the lesson.

Problem 5

3(x + 4)

Problem 6

5(y + 2)

Problem 7

4(a - 3)

Problem 8

6(x - 1)

Problem 9

2(3x + 5)

Problem 10

7(2y - 4)

Problem 11

-2(x + 6)

Problem 12

-3(a - 4)

Problem 13

-(y + 8)

Problem 14

-(x - 5)

Problem 15

10(2x - 3)

Problem 16

4(-3x + 2)

Problem 17

6(y + 4)

Problem 18

5(2x + 3)

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

8(2x + 5)

Problem 20

-5(2y - 3)

Problem 21

-(4x - 7)

Problem 22

6(-2a - 3)

Problem 23

-3(-x + 4)

Problem 24

12(x - 4)

Problem 25

4(x + 5) + 8

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