Answers Algebra II Sum and Difference of Two Cubes — QuizQuestion 4

4

QuizMultiple Choice

Sum and Difference of Two Cubes — Quiz

Question 4 • Algebra II

Which expression is a sum of cubes?

Answer

A

9 A cubed b to the 6th power plus 8 A to the 9th power b to the 12th power

B

27 A cubed b to the 8th power plus 8 A to the 9th power b to the 12th power

C

negative 27 A cubed b to the 6th power plus 8 A to the 9th power b to the 12th power

D

negative 9 A cubed b to the 6th power plus A to the 9th power b to the 10th power

Explanation

A sum of cubes has two terms, each of which is a perfect cube. In choice C, −27A³b⁶ = (−3Ab²)³ and 8A⁹b¹² = (2A³b⁴)³, so both terms are cubes. Therefore, choice C is a sum of cubes.

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