2-8 Inverse of a Sum and SimplifyingWarm-up Problems1. (–1)(–1)2. (–1)x3. (–1)2y4. (–1)(x + 2)

Simplify.5. [(3 + 5) + 7] + 16. (2x + 4x) – 4x7. 2 + 3(5 + 4)8. [(7x – 3x) – 2x] + 5x

Chapter 22-8 Inverse of a Sum and Simplifying

The Property of –1

• For any rational number a,

(Negative one times a is the additive inverse of a.)

1 a a

Example 1

• Rename each additive inverse without parentheses.

( )3 x

1 3 1( )x

3 ( )x

3 x

1(3 )x

Try This

• Multiply.a. –(x + 2)

b. –(5x + 2y + 8)

c. –(a – 7)

d. –(3c – 4d + 1)

The Inverse of a Sum of a Property

• For any rational numbers a and b,

(The additive inverse of a sum is the sum of the additive inverses.)

( ) ( )a b a b

Try This

• Multiply.e. –(6 – t)

f. –(–4a + 3t – 10)

g. –(18 – m – 2n + 4t)

Example 2

• Simplify.

3 4 2x x ( ) 3 4 2x x( ( ))

3 4 2x x( ( ))

3 4 2x x

x 2

Try This

• Multiply.h. 5x – (3x + 9)

i. 5x – 2y – (2y – 3x – 4)

Example 3

• Simplify.

x x y 3( ) x x y( ( ))3

x x y( )3 3

x x y3 3

2 3x y

Try This

• Multiply.j. y – 9(x + y)

k. 5a – 3(7a – 6)

Grouping Symbols

• Parentheses ( )• Brackets [ ]• Braces { }

{ [ ( )]}8 9 12 5 { [ ( )]}8 9 17

{ [ ]}8 8

16

Try This

• Multiply.l. 3(4 + 2) – {7 – [4 – (6 + 5)]}

m. [3(4 + 2) + 2x] – [4(y + 2) – 3(y – 2)]