LESSON Practice B 1-9 Simplifying Algebraic Expressions

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Name

LESSON

Date

Class

Practice B

1-9 Simplifying Algebraic Expressions

Identify like terms in each list.

1. 3a b 2 b 3 4b 2 4 5a

3a and 5a; b 2 and 4b 2

2. x

x4

4x 2

4x

4x 4

3x 2

x and 4x; x 4 and 4x 4; 4x 2 and 3x 2

3. 6m 6m 2 n 2 2n 2 4m 5n

6m and 4m; 2n and 5n

4. 12s 7s 4 9s s 2 5 5s 4 2

12s and 9s; 7s 4 and 5s 4; 5 and 2

Simplify. Justify your steps using the Commutative,

Associative, and Distributive Properties when necessary.

5. 2p  22q 2  p

6. x 2  3x 2  42

2

4x 2  16

7. n 4  n 3  3n  n  n 3

8. 4a  4b  2  2a  5b  1

n 4  2n

9. 32m 2  14n 2  12m 2  5n  3

2a  9b  1

10. 2h 2  3g  2h 2  22  3  4g

20m 2  14n 2  5n  3

7 1

11. Write an expression for the perimeter

of the figure at the right. Then

simplify the expression.

6v ? s

2v  8s  5

2s ? 5

12. Write an expression for the combined

perimeters of the figures at the right.

Then simplify the expression.

a

b?2

14a  2b  4

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

5s ? 4v

68

3a

3a

Holt Mathematics

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Page 115

Practice B

1-9 Simplifying Algebraic Expressions

Practice A

1-9 Simplifying Algebraic Expressions

LESSON

LESSON

Identify like terms in each list.

Identify like terms in each list.

1. 3a b 2 b 3 4b 2 4 5a

1. 6a b a 17 4b 32 17a

3a and 5a; b 2 and 4b 2

6a, a, and 17a; b and 4b; 17 and 32

2. x x 2 3x 3 3x 2 6

2

3. 6m

6z2 and z2; z, 6z, and 17z; 2 and 3

2

8m m

2

12m

2

6m

n 2 2n 2 4m

12sand 9s; 7s 4 and 5s 4; 5 and 2

5. 2p 22p 56q 122 q 34

Simplify. Justify your steps using the Commutative,

Associative, and Distributive Properties when necessary.

2p and 22p; 56q and q; 122 and 34

5. 2p  22q 2  p

6. d d 2 15d 2 2d 42 5d 44

2

d, 2d, and 5d; d and 15d ; 4 and 44

4

3

7. n  n  3n  n  n

7. 6p 2  3p 2

8. 9x  6x

9p 2

2

 14n 2  12m

20m

5h 2  7

13. Find the perimeter of the rectangle.

Combine like terms.

A 4x  3y

B 8x  6y

C 12xy

D 4x 2  3y 2

 14n 2  5n  3

7g  1

6v

s

5s

2s

12. Write an expression for the combined

perimeters of the figures at the right.

Then simplify the expression.

3y

4v

5

a

b

14a  2b  4

Holt Mathematics

Practice C

1-9 Simplifying Algebraic Expressions

3a

2

68

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

Holt Mathematics

LESSON

Simplify each expression. Justify your steps using the Commutative,

Associative,and Distributive Properties, when necessary.

1. 8k 2  4k  3k 2  32  k  5

3a

Reteach

1-9 Simplifying Algebraic Expressions

LESSON

2. 10x 3  5y 2  2xy  4y 2  4xy  x 3

2

Look at the following expressions: x  1x

x  x  2x

x  x  x  3x

The numbers 1, 2, and 3 are called coefficients of x.

9x 3  y 2  6xy

5k  3k  14

2

2

4

4. 12x  6x 2  5x 3  x 2  2xy  8x 4

3. 3a  2b  6c  a  2c  b  c

2

4

3

2

4a  3b  5c

4x  5x  5x  2xy

5. 9p 6  q 2  6p  5q 2  5p  5q 2

6. h 2  4h  4h 2  h  4  h 2  7h

9p 6  q 2  11p

6h 2  10h  4

Identify each coefficient.

3

1. 3n

 5n  4m

3

 2m

3

7

2. 7y

3. m

1

4. 9

0

An algebraic expression has terms that are separated by  and .

In the expression 2x  5y, the terms are 2x and 5y.

7. Write an expression that has five terms and simplifies to

5m 3  4n.

Possible answer: 3m

10. 2h 2  3g  2h 2  22  3  4g

4x

67

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

 5n  3

2v  8s  5

6b 2  7b  10

4x  4y  z

2

2a  9b  1

2

11. Write an expression for the perimeter

of the figure at the right. Then

simplify the expression.

12. 5b  5b  6b 2  10  3b

11. 3x  3y  x  y  z

8. 4a  4b  2  2a  5b  1

n  2n

9. 32m

10. 7h 2  3  2h 2  4

3a 2  6b 2

4x 2  16

3

4

3x

9. a 2  b 2  2a 2  5b 2

n

Expression

Terms

8x  4y

8x and 4y

m  3n

m and 3n

4a 2  2b  a

4a 2, 2b, and a

6d  2p

6d and 2p

x

8. Write and simplify an expression for

the perimeter of the figure to the

right.

y

2y

Sometimes the terms of an expression can be combined.

Only like terms can be combined.

2

1

4y

6x  7y  5

2x

4

7w  w

like terms

2x  2y  2

unlike terms because x and y are different variables

8e  3e  2e like terms

3x

5d  25g

a

9. Write an expression to find the

combined perimeters of the figures

to the right. Then simplify the

expression.

a

a

b

b

3b

5

12a  14b  12

3a

2

4b

7w  w  8w

6y  1  3y  3y  1

Simplify.

5. y  5y

6y

2x  6y  2

69

Copyright ? by Holt, Rinehart and Winston.

unlike terms because d and g are different variables

To simplify an expression:

Step 1: Combine like terms.

Step 2: Add or subtract the coefficients of the variable.

3a

10. Jake scored x points in the first basketball game. He scored

2 fewer points in the next game. His teammate, Jack, scored

2y points in the first game and 4 more than twice as many points

in the next game. Write and simplify an expression for the total

number of points scored by both players.

Copyright ? by Holt, Rinehart and Winston.

All rights reserved.

6. x 2  3x 2  42

p  22q 2

Combine like terms.

3

5n

4. 12s 7s 4 9s s2 5 5s 4 2

18

2

3x 2

4

6m and 4m ; 2n and 5n

8m 2 and m 2; m , 8m , and 12m ; 8 and 18

2

4x 4

xand 4x; x and 4x ; 4x 2 and 3x 2

x and 3x ; xand 3x; 3 and 6

8 8m

4x 2

4x

4

2

3. 2 6z 6z 2 z 17z z 2 3

4. m

x4

2. x

Holt Mathematics

6. 9x  4x

7. 5s  2s

5x

3s

9. 3b  b  6

10. 8a  a  3

4b  6

7a  3

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All rights reserved.

115

8. 3d  7d

10d

11. 2p  4p  r

6p  r

70

12. 9b  8b  c

b c

Holt Mathematics

Holt Mathematics

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