1. Simplifying Expressions AIR Questions Name_______________________________
For each of the questions below, select the appropriate answers. There may be more than one correct
answer for each question.
1. Which of the expressions below are not equivalent to −4(𝑛 + 5)?
a. −4𝑛 − 20
b. −4𝑛 + 20
c. −2(2𝑛 + 10)
d. 2(−2𝑛 − 10)
e. 2(−2𝑛 + 10)
2. Which of the following expressions contains like terms that can be combined?
a. −7𝑥 + 13𝑥 − 4
b. 𝑦 − 4x + z
c. 𝑦 − 4x + y
d. 𝑥2
− 3𝑥 + 10𝑦
e. 4(𝑥 + 9) − 20
3. Which of the following steps are algebraically correct for simplifying the expression
−(𝑥 + 14) + 3(2𝑥 − 1)?
a. −(𝑥) − (14) + 3(2𝑥) − 3(1)
b. −𝑥 + 14 + 6𝑥 − 3
c. −𝑥 − 14 + 5𝑥 − 3
d. −𝑥 − 14 + 6𝑥 − 3
e. −7𝑥 − 17
4. Which of the expressions below are equivalent to 8(𝑎 − 3) + 2(3𝑎 + 9) − 𝑎?
a. 8𝑎 − 24 + 5𝑎 + 18
b. 8𝑎 − 24 + 6𝑎 + 18 − 𝑎
c. 8𝑎 − 24 + 6𝑎 + 18
d. 8𝑎 − 6 + 5𝑎
e. 13𝑎 − 6
5. Which of the following expressions are not simplified completely?
a. 13𝑎 − 4𝑏 + 1
b. 13𝑎 − 4𝑎 + 1
c. 13𝑎 − 4 + 1
d. 13𝑎 − 4𝑏 + 𝑐
e. 13𝑎 − 4 + 𝑐
6. In the expression 4𝑎 − 3(𝑎 + 12𝑎) + 5(𝑏 − 4), which of the following steps can be
carried out first and still produce a correct answer?
a. Distribute 4𝑎 first.
b. Distribute −3 first.
c. Combine 𝑏 and −4 inside the parentheses.
d. Combine the 𝑎 and 12𝑎 inside the parentheses.
e. Combine the −3 and the 5 outside the parentheses.

2. Simplifying Expressions AIR Questions Name_______________________________
7. Which of the following statements correctly describes like terms?
a. Like terms may have different variables.
b. Like terms may have different exponents attached to the variables.
c. Like terms must have the same variables.
d. Like terms must have the same exponents attached to the variables.
e. All numbers without variables are considered like terms.
8. A rectangle has a width, 𝑤, and a length that is three times the size of the width. Which
of the following statements about this rectangle are true?
a. The length can be represented by 3𝑤.
b. The perimeter can be represented by the expression 𝑤 + 3𝑤.
c. The perimeter can be represented by the expression 2(𝑤 + 3𝑤).
d. The perimeter can be represented by the expression 3(𝑤 + 3𝑤).
e. Even if the perimeter or the area of the rectangle are given to you, it is not
enough information to calculate the length of the rectangle.
9. In some high school classes, the final grade can be calculated with the expression
0.70 (
𝑄1+𝑄2+𝑄3+𝑄4
4
) + 0.30(𝐸𝑂𝐶), where Q1, Q2, Q3, and Q4 all represent each report
card grade and EOC represents the End of Course Exam grade. If Jane got 85%, 88%,
82%, and a 90% on her report card grades in Algebra, then scored an 84% on her EOC,
which of the following information would you consider true?
a. The average of Jane’s report card grades is exactly 85.8%.
b. The average of Jane’s report card grades makes up 0.70 (or 70%) of her final
grade in the class.
c. Jane’s EOC grade was lower than the average of her report card grades.
d. Jane’s final grade in the class is greater than her EOC grade.
e. Jane’s final grade in the class is less than her EOC grade.
10. Write at least two equivalent expressions for −6(5𝑥 − 9) + 15. Explain how you know
each one is equivalent to the original expression.
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11. Simplify the expression 3(𝑥 − 4𝑥) − 12𝑥 + (𝑥 + 42). Explain how you know your
answer cannot be simplified any further.
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3. Simplifying Expressions AIR Questions Name_______________________________
Answers:
1. B, E
2. A, C, E
3. A, D
4. A, B, D, E
5. B, C
6. B, D
7. C, D, E
8. A, C
9. B, C, D
10. Answers may vary, and explanations may vary based on the answer provided. A sample
of one equivalent expression would be −30𝑥 + 54 + 15. It is the same as the original
expression because the only change made was distributing the −6 to the inside of the
parentheses.
11. −20𝑥 + 16. I know this is completely simplified because the two terms in this
expression are not like terms. They are not like terms because one term has a variable
and the other does not.