Review of Expessions

Distribution

Ex. 1) Simplify. -3(4x – 2)

-3(4x + -2)

-3(4x) + -3(-2)

-12x + 6

Distribution

Ex. 2) Simplify.

5

28

4

3x

10

36

20

6

4

24

5

2

4

3

1

8

4

3

x

x

x

Combining Like Terms

Ex. 3) Simplify. 9y – 4 – 12y + 7

9y + -4 + -12y + 7

(9 + -12)y + (-4 + 7)

-3y + 3

Distribution and Combining Like Terms

Ex. 4) Simplify. 4(x + 2) + 2(5x + 7)

4x + 8 + 10x + 14

(4 + 10)x + (8 + 14)

14x + 22

Adding linear expressions

Ex. 5) Simplify. (12x + -15) + (-8x + 24)

Rewrite vertically with like terms in columns.

Combine columns.

12x + -15

+ -8x + 24

4x + 9

Subtracting linear expressions

Ex. 6) Simplify. (-6x + 1) – (2x – 5)

Rewrite as addingthe additive inverse.

Rewrite vertically with like terms in columns.

Combine columns.

(-6x + 1) + (-2x + 5)

-6x + 1

+ -2x + 5

-8x + 6

Subtracting linear expressions

Ex. 7) Subtract (-2x + 5) from (-4x – 7).

Rewrite as addingthe additive inverse.

Rewrite vertically with like terms in columns.

Combine columns.

(-4x – 7) + (+2x + -5)

-4x + -7

+ 2x + -5

-2x + -12 = -2x – 12

(-4x – 7) – (-2x + 5)Be careful with order as you set up the subtraction problem!

Factoring expressions

Ex. 8) Factor. 27x + 9

The GCF of 27x and 9 is 9.

9(3x) = 27x and 9(1) = 9

Rewrite the expression as a product of the GCF and a binomial. 9(3x + 1)

Remember, you can check your answer by completing the distribution! 9(3x + 1) = 27x + 9

Factoring expressions

Ex. 9) Factor. 8x – 20

The GCF of 8x and 20 is 4.

4(2x) = 8x and 4(5) = 20

Rewrite the expression as a product of the GCF and a binomial. 4(2x – 5)

Remember, you can check your answer by completing the distribution!

4(2x – 5) = 8x – 20