#### Solved Examples and Worksheet for Simplifying Expressions Using Like Terms

Q1Simplify 8 + 12m - 10.
A. 12m - 2
B. 2m
C. 2m + 12
D. None of the above

Step: 1
8 + 12m - 10 = 12m + 8 - 10
[Arrange like terms.]
Step: 2
= 12m + (8 - 10)
[Use associative property.]
Step: 3
= 12m - 2
[Simplify like terms.]
Correct Answer is :   12m - 2
Q2Simplify 4a + b + 3a - 5b.

A. 4ab
B. 7a - 4b
C. 7a - 5b
D. 7b + 4a

Step: 1
4a + b + 3a - 5b
[Original expression.]
Step: 2
= 4a + 3a + b - 5b
[Arrange like terms.]
Step: 3
= (4a + 3a) + (b - 5b)
[Use associative property.]
Step: 4
= 7a - 4b
[Combine like terms.]
Correct Answer is :   7a - 4b
Q3Simplify:
268m - 32m

A. 268m
B. 236m
C. 236
D. 300m

Step: 1
268m - 32m
[Original expression.]
Step: 2
(268 - 32)m
[Use distributive property.]
Step: 3
= 236m
[Subtract.]
Q4Simplify:
11 + 20m - 14

A. 20m - 3
B. 3m + 20
C. 20m + 3
D. 3m

Step: 1
11 + 20m - 14 = 20m + 11 - 14
[Arrange like terms.]
Step: 2
= 20m + (11 - 14)
[Use associative property.]
Step: 3
= 20m - 3
[Simplify like terms.]
Correct Answer is :   20m - 3
Q5Simplify:
5a + 1 + 2a - 7

A. 7a - 6
B. 3a
C. 7 + 6a
D. 7a - 7

Step: 1
5a + 1 + 2a - 7
[Original expression.]
Step: 2
= (5a + 2a) + (1 - 7)
[Group the like terms.]
Step: 3
= 7a - 6
[Simplify and retain the unknowns.]
Step: 4
So, 5a + 1 + 2a - 7 = 7a - 6
Correct Answer is :   7a - 6
Q6Simplify 12 + 20m - 15.

A. 3m
B. 3m + 20
C. 20m - 3
D. None of the above

Step: 1
12 + 20m - 15 = 20m + 12 - 15
[Arrange like terms.]
Step: 2
= 20m + (12 - 15)
[Combine like terms.]
Step: 3
= 20m - 3
[Simplify like terms.]
Correct Answer is :   20m - 3
Q7Simplify the following expression by combining like terms:
3y - 5xy + 7y - 8xy

A. - 10y - 13xy
B. - 10 y - 3xy
C. 10y - 3xy
D. 10y - 13xy

Step: 1
3y - 5xy + 7y - 8xy
[Original Expression.]
Step: 2
= (3y + 7y) - (5xy + 8xy) = 10y - 13xy
[Combine like terms.]
Step: 3
∴ 3y - 5xy + 7y - 8xy = 10y - 13xy
[Simplify.]
Correct Answer is :   10y - 13xy
Q8Simplify the following expression by combining like terms:
- 2x + 4xy + 8x - 1 - 13xy

A. - 6x + 9xy - 1
B. 6x - 9xy - 1
C. 6x + 9xy - 1
D. - 6x - 9xy - 1

Step: 1
-2x + 4xy + 8x - 1 - 13xy
[Original expression.]
Step: 2
= (-2x + 8x) + (4xy - 13xy) - 1 = 6x - 9xy - 1
[Combine like terms.]
Step: 3
∴ - 2x + 4xy + 8x - 1 - 13xy = 6x - 9xy - 1
[Simplify.]
Correct Answer is :   6x - 9xy - 1
Q9Simplify the following expression by combining like terms:
- 3x + 4y + 5xy - 9y + 2x - 7xy

A. - x + 5y - 2xy
B. x - 5y - 12 xy
C. - x - 13y - 2xy
D. - x - 5y - 2xy

Step: 1
- 3x + 4y + 5xy - 9y + 2x - 7xy
[Original expression.]
Step: 2
= (- 3x +2x) + (4y - 9y) + (5xy - 7xy) = - x - 5y - 2xy
[Combine like terms.]
Step: 3
∴ - 3x + 4y + 5xy - 9y + 2x - 7xy = - x - 5y - 2xy
[Simplify.]
Correct Answer is :    - x - 5y - 2xy