3
QuizMultiple Choice

Sum and Difference of Two Cubes — Quiz

Question 3 • Algebra II

Which expression is a perfect cube?

Answer
A
negative 216 x to the 9th power y to the 18th power
B
negative 125 x to the 9th power y to the 20th power
C
negative 8 x to the 21th power y to the 8th power
D
negative 64 x to the 64th power y to the 64th power

Explanation

A monomial is a perfect cube when its coefficient is an integer cube and each variable’s exponent is divisible by 3. In choice A, −216 = (−6)³, and both 9 and 18 are divisible by 3, so the expression is (−6x³y⁶)³. The other choices have at least one variable exponent that is not divisible by 3.

AI-written and checked against the verified answer.

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