Simplify.

Warm-Up Exercises

ANSWER 23 +( )22 ( ),16 $98

ANSWER 15x3 –

ANSWER 166y 2 +

1. ( )5x3 –

2. ( )4+6 y 2 8–

You bought 3 DVDs for $22 each and 2 CDs for $16 each. Write and simplify an expression for the total cost.

3.

Identify Terms in an ExpressionExample 1

Identify the terms in the expression .11– 2x 2 –7x–

11– 2x 2–7x– = 11– ( )7x– 2x 2–( )+ +

ANSWER

The terms of the expression are .11,– 2x 2–7x, and–

Write the expression as a sum.

SOLUTION

Identify Coefficients and Like TermsExample 2

Identify the coefficients and like terms in the expression .

–x 2 7x– + 5 3x 2– 10–

Begin by writing the expression as a sum in order to identify the terms.

SOLUTION

x 2 7x– + 5 3x 2– 10– ( )10–3x 2–( )x 2 + 5( )7x–+ + +=

ANSWER

The coefficients of the expression are 1, 7, and 3. The terms x 2 and 3x 2 are like terms. The terms 5 and 10 are also like terms.

– ––

–

Identify the terms, coefficients, and like terms in the expression

Checkpoint

4x 3 9x–+5x 2– x 2 9x 3 7x.– +

Identify Terms, Coefficients, and Like Terms

ANSWER

terms: 4x 3, 5x 2, x 2, 9x, 9x 3, 7x;– – –

like terms: 4x 3 and 9x 3, 5x 2 and x 2, 9x and 7x– – –

coefficients: 4, 5, 1, 9, 9, 7;– – –

1.

Example 3 Simplify by Combining Like Terms

Simplify the expression.

9x+5xa.

2x2 + –3x x2 + 6xb.

7x4yc.

– – 3x+12y

Add.14x=

SOLUTION

9x+5xa.

( )9+5 x= Distributiveproperty

Example 3 Simplify by Combining Like Terms

Distributive property

2 +– xx2 + 3( ) ( )= 1 6

9x x2 += Add or subtract.

7x4yc.

– – 3x+12y 4y( )= – 12y 7x+ + 3x( )– Group like terms.

4( )= – 12 7+ + 3( )–y x Distributiveproperty

= –8y – 4x Add or subtract.

2x2 +– 6xx2 + 3x( ) ( ) Group like terms.

2x2 + –3x x2 + 6xb.

=

Example 4 Simplify Expressions with Grouping Symbols

Simplify the expression.

b.

512a.

– –( )1x 4 –( )x6 3 –( )8x+

Group like terms.

– +5x= ( )5+12

Add.– +5x= 17

SOLUTION

512a.

– –( )1x – 5+5x= 12 Distributiveproperty

Example 4 Simplify Expressions with Grouping Symbols

= Group like terms.

( )4x– 3x+ ( )+ – 2424

= Distributiveproperty

( )4– 3+ ( )+ – 2424x

= Add or subtract.

x–

b.

4 –( )x6 3 –( )8x+ – 4x24 3x – 24+= Distributiveproperty

Checkpoint

2. ANSWER 4x3x7x –

3. x1 + 810x –+ ANSWER 711x –

4. x + x2 – 4x2 – 5x ANSWER –3x2 – 4x

Simplify the expression.

5. 3 + ( )4+x2 ANSWER 11+2x

6. x ( )2x6– – ANSWER –5x + 12

Simplify Expressions

Checkpoint

Simplify the expression.

7. ( )1x3 – ANSWER 2x + 6– ( )9x –

Simplify Expressions

Example 5 Use a Real-Life Model

Rowboat Rentals A boat rental company charges customers for rowboats as shown in the advertisement. There is a 1 hour minimum rental time.

a. Write and simplify an expression that gives the total cost to rent a rowboat for h hours, where .1h ≥

b. Find the total cost of renting a rowboat for 8 hours.

Example 5 Use a Real-Life Model

(dollars per hour)

LABELS Cost for first hour 13= (dollars)

Cost for each additional hour 6=

Number of additionalhours =

(hours)1h –

SOLUTION

VERBALMODEL

Cost for first

hour

Number ofadditional

hours•

a. Cost for each additional

hour+

Example 5 Use a Real-Life Model

ALGEBRAICMODEL

=13 + ( )16 h – 13 + 66h –

= 13+ 66h –

= 7+6h

ANSWER

The total cost of renting a rowboat for 1 hour or longeris given by the expression .76h +

b. To find the total cost of renting a rowboat for 8 hours, evaluate the expression for .8h =

76h + Substitute 8 for h.= 7+( )86

Example 5 Use a Real-Life Model

Multiply.= 7+48

Add.= 55

ANSWER

Renting a rowboat for 8 hours will cost $55.

Checkpoint

A calling card charges $1 for all phone calls up to 15 minutes and $.25 for each additional minute.

8. Write and simplify an expression that gives the total cost of a phone call that lasts m minutes, where m is at least 15.

ANSWER , or1 + ( )150.25 m – 2.750.25m –

9. Use your answer from Exercise 8 to find the total cost of a phone call that lasts for 28 minutes.

ANSWER $4.25

Use a Real-Life Model

Checkpoint

A calling card charges $1 for all phone calls up to 15 minutes and $.25 for each additional minute.

10. Use your answer from Exercise 8 to find the total cost of a phone call that lasts for 1 hour 10 minutes.

ANSWER $14.75

Use a Real-Life Model