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Pre-Algebra

Distributive Property

Lesson

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

a(b+c)=ab+aca(b + c) = ab + ac
a(b−c)=ab−aca(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)3(x + 4)

Multiply 3 by each term inside:

=3⋅x+3⋅4= 3 \cdot x + 3 \cdot 4
=3x+12= 3x + 12

Worked example 2

−2(y−5)-2(y - 5)

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

=−2⋅y+(−2)⋅(−5)= -2 \cdot y + (-2) \cdot (-5)
=−2y+10= -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)2(x + 1)

Problem 2

3(y+5)3(y + 5)

Problem 3

4(a+2)4(a + 2)

Problem 4

5(x−1)5(x - 1)

Practice

Standard problems matching the lesson.

Problem 5

3(x+4)3(x + 4)

Problem 6

5(y+2)5(y + 2)

Problem 7

4(a−3)4(a - 3)

Problem 8

6(x−1)6(x - 1)

Problem 9

2(3x+5)2(3x + 5)

Problem 10

7(2y−4)7(2y - 4)

Problem 11

−2(x+6)-2(x + 6)

Problem 12

−3(a−4)-3(a - 4)

Problem 13

−(y+8)-(y + 8)

Problem 14

−(x−5)-(x - 5)

Problem 15

10(2x−3)10(2x - 3)

Problem 16

4(−3x+2)4(-3x + 2)

Challenge

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

Problem 17

8(2x+5)8(2x + 5)

Problem 18

−5(2y−3)-5(2y - 3)

Problem 19

−(4x−7)-(4x - 7)

Problem 20

6(−2a−3)6(-2a - 3)

Problem 21

−3(−x+4)-3(-x + 4)

Problem 22

12(x−4)12(x - 4)