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Sum and Difference of Two Cubes

Question 1 • AZ-Common Core Algebra II A

Choose the expressions that are perfect cubes.

Answer
A
–3
B
125a6
C
8m20
D
100w24x3
E
–64q12
F
–c30d9f18g3

Explanation

A perfect-cube monomial has a coefficient that is a perfect cube and variable exponents that are all multiples of 3. In B, 125 = 5³ and 6 is a multiple of 3. In E, −64 = (−4)³ and 12 is a multiple of 3; F also qualifies because −1 is a perfect cube and all its exponents are multiples of 3. C has an exponent of 20, and D has a coefficient of 100, so neither is a perfect cube.

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