8
QuizMultiple Choice

Sum and Difference of Two Cubes — Quiz

Question 8 • Algebra II

Which expression is a perfect cube?

Answer
A
negative 1 comma 452 m to the 18th power n to the 15th power p to the 22th power
B
1 comma 331 m to the 18th power n to the 15th power p to the 22th power
C
1 comma 452 m to the 18th power n to the 15th power p to the 21th power
D
negative 1 comma 331 m to the 18th power n to the 15th power p to the 21th power

Explanation

For an expression to be a perfect cube, its numerical coefficient must be a perfect cube and each variable’s exponent must be divisible by 3. Since 1,331 = 11³ and 18, 15, and 21 are all divisible by 3, the expression with coefficient −1,331 and p²¹ is a perfect cube: it is the cube of −11m⁶n⁵p⁷.

AI-written and checked against the verified answer.

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