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Sum and Difference of Two Cubes

Question 1 • AZ-Common Core Algebra II A

Which expressions are perfect cubes?

Answer
A
–1,000
B
27r21
C
343p
D
g3h30
E
–1

Explanation

A perfect cube can be written as a quantity raised to the third power. Since −1,000 = (−10)³, choice A is a perfect cube. Also, 27r²¹ = (3r⁷)³ and g³h³⁰ = (gh¹⁰)³, so B and D are perfect cubes. Finally, −1 = (−1)³; 343p is not generally a perfect cube because the exponent on p is 1.

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