Solved Examples and Worksheet for Simplifying Expressions Using Like Terms
Q1
Simplify
8 + 12
m
- 10.
A
. 12
m
- 2
B
. 2
m
C
. 2
m
+ 12
D
. None of the above
Solutions
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Step: 1
8 + 12
m
- 10 = 12
m
+ 8 - 10
[Arrange like terms.]
Step: 2
= 12
m
+ (8 - 10)
[Use associative property.]
Step: 3
= 12
m
- 2
[Simplify like terms.]
Correct Answer is :
12
m
- 2
Q2
Simplify
4
a
+
b
+ 3
a
- 5
b
.
A
. 4
ab
B
. 7
a
- 4
b
C
. 7
a
- 5
b
D
. 7
b
+ 4
a
Solutions
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Step: 1
4
a
+
b
+ 3
a
- 5
b
[Original expression.]
Step: 2
= 4
a
+ 3
a
+
b
- 5
b
[Arrange like terms.]
Step: 3
= (4
a
+ 3
a
) + (
b
- 5
b
)
[Use associative property.]
Step: 4
= 7
a
- 4
b
[Combine like terms.]
Correct Answer is :
7
a
- 4
b
Q3
Simplify:
268
m
- 32
m
A
. 268
m
B
. 236
m
C
. 236
D
. 300
m
Solutions
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Step: 1
268
m
- 32
m
[Original expression.]
Step: 2
(268 - 32)
m
[Use distributive property.]
Step: 3
= 236
m
[Subtract.]
Correct Answer is :
236
m
Q4
Simplify:
11 + 20
m
- 14
A
. 20
m
- 3
B
. 3
m
+ 20
C
. 20
m
+ 3
D
. 3
m
Solutions
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Step: 1
11 + 20
m
- 14 = 20
m
+ 11 - 14
[Arrange like terms.]
Step: 2
= 20
m
+ (11 - 14)
[Use associative property.]
Step: 3
= 20
m
- 3
[Simplify like terms.]
Correct Answer is :
20
m
- 3
Q5
Simplify:
5
a
+ 1 + 2
a
- 7
A
. 7
a
- 6
B
. 3
a
C
. 7 + 6
a
D
. 7
a
- 7
Solutions
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Step: 1
5
a
+ 1 + 2
a
- 7
[Original expression.]
Step: 2
= (5
a
+ 2
a
) + (1 - 7)
[Group the like terms.]
Step: 3
= 7
a
- 6
[Simplify and retain the unknowns.]
Step: 4
So, 5
a
+ 1 + 2
a
- 7 = 7
a
- 6
Correct Answer is :
7
a
- 6
Q6
Simplify
12 + 20
m
- 15.
A
. 3
m
B
. 3
m
+ 20
C
. 20
m
- 3
D
. None of the above
Solutions
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Step: 1
12 + 20
m
- 15 = 20
m
+ 12 - 15
[Arrange like terms.]
Step: 2
= 20
m
+ (12 - 15)
[Combine like terms.]
Step: 3
= 20
m
- 3
[Simplify like terms.]
Correct Answer is :
20
m
- 3
Q7
Simplify the following expression by combining like terms:
3
y
- 5
xy
+ 7
y
- 8
xy
A
. - 10
y
- 13
xy
B
. - 10
y
- 3
xy
C
. 10
y
- 3
xy
D
. 10
y
- 13
xy
Solutions
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Step: 1
3
y
- 5
xy
+ 7
y
- 8
xy
[Original Expression.]
Step: 2
= (3
y
+ 7
y
) - (5
xy
+ 8
xy
) = 10
y
- 13
xy
[Combine like terms.]
Step: 3
∴ 3
y
- 5
xy
+ 7
y
- 8
xy
= 10
y
- 13
xy
[Simplify.]
Correct Answer is :
10
y
- 13
xy
Q8
Simplify the following expression by combining like terms:
- 2
x
+ 4
xy
+ 8
x
- 1 - 13
xy
A
. - 6
x
+ 9
xy
- 1
B
. 6
x
- 9
xy
- 1
C
. 6
x
+ 9
xy
- 1
D
. - 6
x
- 9
xy
- 1
Solutions
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Step: 1
-2
x
+ 4
xy
+ 8
x
- 1 - 13
xy
[Original expression.]
Step: 2
= (-2
x
+ 8
x
) + (4
xy
- 13
xy
) - 1 = 6
x
- 9
xy
- 1
[Combine like terms.]
Step: 3
∴ - 2
x
+ 4
xy
+ 8
x
- 1 - 13
xy
= 6
x
- 9
xy
- 1
[Simplify.]
Correct Answer is :
6
x
- 9
xy
- 1
Q9
Simplify the following expression by combining like terms:
- 3
x
+ 4
y
+ 5
xy
- 9
y
+ 2
x
- 7
xy
A
. -
x
+ 5
y
- 2
xy
B
.
x
- 5
y
- 12
xy
C
. -
x
- 13
y
- 2
xy
D
. -
x
- 5
y
- 2
xy
Solutions
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Step: 1
- 3
x
+ 4
y
+ 5
xy
- 9
y
+ 2
x
- 7
xy
[Original expression.]
Step: 2
= (- 3
x
+2
x
) + (4
y
- 9
y
) + (5
xy
- 7
xy
) = -
x
- 5
y
- 2
xy
[Combine like terms.]
Step: 3
∴ - 3
x
+ 4
y
+ 5
xy
- 9
y
+ 2
x
- 7
xy
= -
x
- 5
y
- 2
xy
[Simplify.]
Correct Answer is :
-
x
- 5
y
- 2
xy
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