LESSON
Simplifying Algebraic Expressions
1-9
Lesson Objectives
Simplify algebraic expressions
Vocabulary
term (p. 42)
coefficient (p. 42)
Additional Examples
Example 1
Identify like terms in the list.
3t
5w 2
7t
9v
4w 2
Look for like
3t
5w 2
8v
with like
7t
9v
4w 2
.
8v
Like terms:
Example 2
Simplify. Justify your steps using the Commutative, Associative, and
Distributive Properties when necessary.
A. 6t 4t
6t and 4t are
6t 4t
terms.
the coefficients.
B. 45x 37y 87
In this expression, there are
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to combine.
20
Holt Mathematics
LESSON
Simplifying Algebraic Expressions
1-9
Lesson Objectives
Simplify algebraic expressions
Vocabulary
term (p. 42) A number, a variable, or a product of numbers and variables that
are separated by plus and minus signs.
coefficient (p. 42) The number that is multiplied by the variable in an algebraic
expression.
Additional Examples
Example 1
Identify like terms in the list.
3t
5w 2
7t
9v
4w 2
Look for like variables
3t
5w 2
7t
9v
Like terms: 3t and 7t
8v
with like powers
4w 2
.
8v
5w 2 and 4w 2
9v and 8v
Example 2
Simplify. Justify your steps using the Commutative, Associative, and
Distributive Properties when necessary.
A. 6t 4t
6t 4t
6t and 4t are like
Subtract
terms.
the coefficients.
2t
B. 45x 37y 87
In this expression, there are no like terms
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20
to combine.
Holt Mathematics
LESSON 1-9 CONTINUED
Example 3
2x + 3
3x + 2
Write an expression for the perimeter of the
triangle. Then simplify the expression.
x
x 3x 2 2x 3
Write an
using the side lengths.
(
)(
)
Identify and
like terms.
like terms.
Try This
1. Identify like terms in the list.
2x
4y 3
8x
5z
5y 3
8z
2. Simplify. Justify your steps using the Commutative, Associative, and
Distributive Properties when necessary.
4x 2 4y 3x 2 4y 2x 2 5
3. Write an expression for the perimeter of the triangle.
Then simplify the expression.
2x + 1
2x + 1
x
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21
Holt Mathematics
LESSON 1-9 CONTINUED
Example 3
2x + 3
3x + 2
Write an expression for the perimeter of the
triangle. Then simplify the expression.
x
Write an expression
x 3x 2 2x 3
using the side lengths.
( x
3x
2x
)( 2
3 )
Identify and group
like terms.
6x 5
Combine
like terms.
Try This
1. Identify like terms in the list.
2x
4y 3
8x
5z
2x and 8x 4y 3 and 5y 3
5y 3
8z
5z and 8z
2. Simplify. Justify your steps using the Commutative, Associative, and
Distributive Properties when necessary.
4x 2 4y 3x 2 4y 2x 2 5
9x 2 5
3. Write an expression for the perimeter of the triangle.
Then simplify the expression.
2x + 1
2x + 1
2x 1 2x 1 x ; 5x 2
x
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21
Holt Mathematics
MSM07G7_RESBK_Ch01_067-074.pe
1/16/06
12:43 PM
Page 70
Name
LESSON
Date
Class
Reteach
1-9 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.
Identify each coefficient.
3
1. 3n
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.
Expression
Terms
8x 4y
8x and 4y
m 3n
m and 3n
2
4a 2b a
4a 2, 2b, and a
6d 2p
6d and 2p
Sometimes the terms of an expression can be combined.
Only like terms can be combined.
7w w
like terms
2x 2y 2
unlike terms because x and y are different variables
8e 3e 2e like terms
5d 25g
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.
7w w 8w
6y 1 3y 3y 1
Simplify.
5. y 5y
6
6. 9x 4x
7. 5s 2s
8. 3d 7d
5x
3s
10d
9. 3b b 6
10. 8a a 3
4b 6
7a 3
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11. 2p 4p r
6p r
70
12. 9b 8b c
bc
Holt Mathematics
2.1 CRB 4-up 99-
1/16/06
2:30 PM
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
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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
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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.
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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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115
8. 3d 7d
10d
11. 2p 4p r
6p r
70
12. 9b 8b c
b c
Holt Mathematics
Holt Mathematics
MSM07G7_RESBK_Ch01_067-074.pe
1/16/06
12:43 PM
Page 68
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
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5s ⫺ 4v
68
3a
3a
Holt Mathematics
2.1 CRB 4-up 99-
1/16/06
2:30 PM
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
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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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115
8. 3d 7d
10d
11. 2p 4p r
6p r
70
12. 9b 8b c
b c
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Holt Mathematics