
Click
Name
LESSON
Here
Date
Class
Practice B
2-9 Combining Like Terms
Identify like terms.
1. 3a b 2 b 3 4b 2 4 5a
2. x
x4
4x
4x 2
4x 4
3x 2
3. 6m 6m 2 n 2 2n 2 4m 5n
4. 12s 7s 4 9s s 2 5 5s 4 2
Combine like terms.
5. 2p ! 22q 2 " p
6. x 2 ! 3x 2 " 42
7. n 4 ! n 3 ! 3n " n " n 3
8. 4a ! 4b ! 2 " 2a ! 5b " 1
9. 32m 2 ! 14n 2 " 12m 2 ! 5n " 3
10. 2h 2 ! 3g " 2h 2 ! 22 " 3 ! 4g
11. Write an expression for the perimeter
of the figure at right. Combine like
terms in the expression.
6v ! s
5s " 4v
2s ! 5
12. Write an expression for the combined
perimeters of the figures at right.
Combine like terms in the
expression.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a
b!2
85
3a
3a
Holt Middle School Math Course 2
Practice B
2-9 Combining Like Terms
Practice A
2-9 Combining Like Terms
LESSON
LESSON
Identify like terms.
Identify like terms.
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
2. x
6
x4
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
Combine like terms.
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
2
5h ! 7
4x ! 4y ! z
6b ! 7b " 10
4x
6v ! s
5s " 4v
2s ! 5
a
3a
b!2
3a
14a ! 2b ! 4
Holt Middle School Math Course 2
Practice C
2-9 Combining Like Terms
85
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Middle School Math Course 2
Reteach
2-9 Combining Like Terms
LESSON
LESSON
Combine like terms.
1. 8k 2 ! 4k " 3k 2 ! 32 " k ! 5
2. 10x 3 ! 5y 2 ! 2xy " 4y 2 ! 4xy " x 3
5k 2 ! 3k ! 14
9x 3 ! y 2 ! 6xy
3. 3a ! 2b 2 ! 6c ! a " 2c ! b 2 ! c
4. 12x 4 ! 6x 2 ! 5x 3 " x 2 ! 2xy " 8x 4
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.
1. 3n
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
3
3
3
3
Possible answer: 3m ! 5n ! 4m " 2m " n
8. Write an expression for the perimeter
of the figure to the right. Combine like
terms in the expression.
x
y!2
2y " 1
6x ! 7y ! 5
4y
a!b
3b ! 5
12a ! 14b ! 12
0
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
like terms
2x " 2y ! 2
unlike terms because x and y are different variables
3a ! 2
4b
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
3a
Combine like terms.
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 an expression for the total number of
points scored by both players and combine like terms.
5. y ! 5y
6y
2x ! 6y ! 2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
4. 9
7w ! w
5d ! 25g
a
86
1
8e " 3e ! 2e like terms
3x
a!b
3. m
Sometimes the terms of an expression can be combined.
Only like terms can be combined.
2x ! 4
9. Write an expression to find the
combined perimeters of the figures to
the right. Combine like terms in the
expression.
7
2. 7y
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 when you combine like terms.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
7g ! 1
12. Write an expression for the combined
perimeters of the figures at right.
Combine like terms in the
expression.
3y
84
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
10. 2h ! 3g " 2h 2 ! 22 " 3 ! 4g
2v ! 8s ! 5
2
13. Find the perimeter of the rectangle.
Combine like terms.
A 4x ! 3y
B 8x ! 6y
!
C 12xy
D 4x 2 ! 3y 2
2
11. Write an expression for the perimeter
of the figure at right. Combine like
terms in the expression.
12. 5b ! 5b ! 6b 2 " 10 " 3b
11. 3x ! 3y ! x ! y ! z
2
20m 2 ! 14n 2 ! 5n " 3
10. 7h 2 ! 3 " 2h 2 ! 4
2
2a ! 9b ! 1
2
9. 32m ! 14n " 12m ! 5n " 3
3x
9. a 2 ! b 2 ! 2a 2 ! 5b 2
8. 4a ! 4b ! 2 " 2a ! 5b " 1
n 4 ! 2n
8. 9x " 6x
2
3a ! 6b
4x 2 " 16
7. n 4 ! n 3 ! 3n " n " n 3
Combine like terms.
2
6. x 2 ! 3x 2 " 42
p ! 22q 2
d, 2d, and 5d; d 2 and 15d 2; 42 and 44
9p
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
7. 6p ! 3p
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 Middle School Math Course 2
6. 9x " 4x
7. 5s " 2s
5x
3s
9. 3b ! b ! 6
10. 8a " a " 3
4b ! 6
7a " 3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
147
8. 3d ! 7d
10d
11. 2p ! 4p ! r
6p ! r
87
12. 9b " 8b ! c
b!c
Holt Middle School Math Course 2
Holt Middle School Math Course 2