Name
LESSON
Date
Class
Practice C
11-2 Simplifying Algebraic Expressions
Simplify each expression. Justify your steps using the Commutative,
Associative,and Distributive Properties, when necessary.
1. 8k 2 4k 3k 2 32 k 5
2. 10x 3 5y 2 2xy 4y 2 4xy x 3
3. 3a 2b 2 6c a 2c b 2 c
4. 12x 4 6x 2 5x 3 x 2 2xy 8x 4
5. 9p 6 q 2 6p 5q 2 5p 5q 2
6. h 2 4h 4h 2 h 4 h 2 7h
7. Write an expression that has five terms and simplifies to
5m 3 4n.
8. Write and simplify an expression for
the perimeter of the figure to the
right.
x
y2
2y 1
4y
2x 4
3x
a
9. Write an expression to find the
combined perimeters of the figures
to the right. Then simplify the
expression.
ab
ab
3b 5
3a 2
4b
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.
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15
Holt Mathematics
Practice B
LESSON
11-2 Simplifying Algebraic Expressions
Practice A
LESSON
11-2 Simplifying Algebraic Expressions
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
2
x4
2. x
6
3x 2
4
3. 6m 6m 2 n 2 2n 2 4m 5n
6z 2 and z 2; z, 6z, and 17z; 2 and 3
6m and 4m; 2n and 5n
4. 12s 7s 4 9s s 2 5 5s 4 2
4. m 8 8m 2 8m m 2 12m 18
12s and 9s; 7s 4 and 5s 4; 5 and 2
8m 2 and m 2; m, 8m, and 12m; 8 and 18
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
2
d, 2d, and 5d; d and 15d ; 4 and 44
6. x 2 3x 2 42
p 22q 2
Combine like terms.
4
3
7. n n 3n n n
7. 6p 2 3p 2
8. 9x 6x
9p 2
n 2n
5s 4v
2s 5
4x
12. Write an expression for the combined
perimeters of the figures at the right.
Then simplify the expression.
3y
a
Holt Mathematics
Holt Mathematics
Review for Mastery
LESSON
11-2 Simplifying Algebraic Expressions
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.
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
14
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Practice C
LESSON
11-2 Simplifying Algebraic Expressions
3a
b2
14a 2b 4
13
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All rights reserved.
6v s
2v 8s 5
6b 2 7b 10
13. Find the perimeter of the rectangle.
Combine like terms.
A 4x 3y
B 8x 6y
C 12xy
D 4x 2 3y 2
7g 1
11. Write an expression for the perimeter
of the figure at the right. Then
simplify the expression.
12. 5b 5b 6b 2 10 3b
4x 4y z
2a 9b 1
10. 2h 2 3g 2h 2 22 3 4g
20m 2 14n 2 5n 3
5h 2 7
11. 3x 3y x y z
8. 4a 4b 2 2a 5b 1
9. 32m 2 14n 2 12m 2 5n 3
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
2. 10x 3 5y 2 2xy 4y 2 4xy x 3
9x 3 y 2 6xy
2
5k 3k 14
3. 3a 2b 2 6c a 2c b 2 c
4. 12x 4 6x 2 5x 3 x 2 2xy 8x 4
4a 3b 2 5c
4x 4 5x 3 5x 2 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
3
3
3
Possible answer: 3m 5n 4m 2m n
8. Write and simplify an expression for
the perimeter of the figure to the
right.
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.
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
Sometimes the terms of an expression can be combined.
Only like terms can be combined.
y2
2y 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.
3b 5
3a 2
4b
7w w 8w
6y 1 3y 3y 1
3a
Simplify.
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.
5. y 5y
6y
2x 6y 2
15
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All rights reserved.
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.
ab
ab
12a 14b 12
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4x 4
x and 4x; x and 4x ; 4x 2 and 3x 2
x and 3x ; x and 3x; 3 and 6
3. 2 6z 6z 2 z 17z z 2 3
2
4x 2
4x
4
2
Holt Mathematics
7. 5s 2s
5x
3s
9. 3b b 6
10. 8a a 3
4b 6
7a 3
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91
6. 9x 4x
8. 3d 7d
10d
11. 2p 4p r
6p r
16
12. 9b 8b c
bc
Holt Mathematics
Holt Mathematics