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Interpreting Structure in Expressions Study Guide
For problems 1 and 2, identify the terms, coefficients, constants, and factors of the given expressions.
1. 32a³ + 14a² + 4a – 6
Terms; 32a³, 14a², 4a, – 6
Coefficients; 32, 14, 4
Constant; -6
Factors; 32 and a³, 14 and a², 4 and a
2. 11x²+ 3x – 7x² + 9
Terms; 4x²+ 3x + 9
Coefficients; 4, 3
Constant; 9
Factors; 4 and x², 3 and x
For problem 3, translate the verbal expression to an algebraic expression. Then, identify the terms,
coefficients, and constants of the given expressions.
3. Half the difference of x and y increased by two-fifth y
1
2
(𝑥 − 𝑦) + 𝑦
2
1
5
1
2
𝑥 − 2𝑦 + 5𝑦
2
1
2
1
5
4
𝑥 − 10 𝑦 + 10 𝑦
1
𝑥 − 10 𝑦
2
1
Terms: 2 𝑥,
1
𝑦
10
1
Coefficients: 2 ,
1
10
1
Factor; 2 𝑎𝑛𝑑 𝑥,
1
10
𝑎𝑛𝑑 𝑦
4. Write an expression with 4 terms, containing the coefficients 7, 11, and 15.
Answers will vary. Possible answer: 7a³ + 11a² - 15a – 6
For problems 5–7, write an algebraic expression to describe each situation. Then, identify the terms,
coefficients, constants, and factors.
5. Alex agrees to buy a 12-month package deal of monthly spa passes, and in turn receives a 20% discount.
Write an algebraic expression to represent the total cost of the monthly passes with the discount, if x represents
the cost of each monthly pass. 12x - .20(12x)
12x – 2.4x
9.6x
6. Sam purchased 8 textbooks from an online store and received a 15% discount. Shipping cost $3.99. Write an
algebraic expression to represent the total cost of the textbooks with the shipping cost, if x represents the cost of
each book. 8x -.15(8x) + 3.99
8x – 1.2x + 3.99
6.8x + 3.99
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7. The area of a triangle with base b and height h is half the product of the base and the height.
𝑏ℎ
2
8. A transfer station charges $12 for a waste disposal permit and an additional $7 for each cubic yard of garbage
it disposes of. This relationship can be described using the expression 12 + 7x. What effect, if any, does
changing the value of x have on the cost of the permit?
Changing the value of x will have no effect on the cost of the permit
9. The product of 5, x, and y is represented by the expression 5xy. If the value of x is negative, what can be said
about the value of y in order for the product to remain negative?
The value of y must be positive
10. A bank account balance for an account with an initial deposit of P dollars earns interest at an annual rate of
r. The amount of money in the account after a years is described using the following expression: P(1 + r)ª.
What effect, if any, does increasing the value of P have on the amount of money after a years?
An increase in the value of P will result in an increase in the amount of money after a years
11. For what values of a will the result of 2ª be greater than 1?
a > 0 (values must be positive)