The Distributive Property & Combining Like Terms

Distributive Property

For any numbers

2(b + c) = 2b + 2c and (b – c)3 = b3 – c3

When a number or letter is separated by parentheses and there are no other operation symbols – it means to distribute by multiplying the numbers or variables together.

= 3b -3c

Use the Distributive Property

Simplify 5(3n + 4)No symbol between the 5 and the parenthesis indicates a multiplication problem.

Distribute by multiplication then perform the indicated operation inside the parenthesis.

)43(5 n )3(5 n

)4(5

n15 20Simplified

Simplify 4(7n + 2) +6No symbol between the 4 and the parenthesis indicates a multiplication problem.

Use the Distributive Property

6)27(4 n )7(4 n

)2(4 n28 8

6

€

6

n28 14Simplified

Notice that 28n cannot be

combined with any other n

terms

The constant terms 8 and 6 are linked with addition and can be combined to form the

constant number 14

Simplify 3(n + 2) + nUse the Distributive Property

nn )2(3 )(3 n

)2(3 n3 6

)(1 n

)(1 n

n4 6Simplified

Combine like terms with parenthesis…

153238 ff

15968 ff

614 f

BACK

Simplify using the distributive property.1)

2)

3)

5(x 3)5 3

5x 15

6(y 7)6 7

6y 42

3(m 8)3 8

3m 24

5 x

6 y

3 m

4)

5)

6)

7(8 x)7 8 7 x

56 7x

x(a b c) x a x b x c

ax bx cx

4(3 m k) 4 3 4 m 4 k

12 4m 4k

Simplify using the distributive property.1)

2)

3)

4(x 7)4 7

4x 28

y(y 3)y 3

2y 3y

x(2x 9)x 9

22x 9x

4 x

y y

x 2x

4)

5)

6)

4(3 y)4 3 4 y

12 4y

10(x 7)10 x 10 7

10x 70

4(k 2)4 k 4 2

4k 8