10
QuizMultiple Choice

Factoring Polynomials: Sum and Difference of Cubes

Question 10 • FL-1200700-Mathematics for College Algebra MIS

A and B are monomials where A = 125 and B = 27p12. What is the factored form of A – B?

Answer
A
(5 – 3p4)(25 + 15p4 + 9p8)
B
(25 – 3p4)(5 + 15p3 + 9p3)
C
(25 – 3p4)(5 + 15p4 + 3p8)
D
(5 – 3p4)(25 + 15p3 + 3p4)

Explanation

Rewrite 125 as 5³ and 27p¹² as (3p⁴)³. Using the difference-of-cubes rule, x³ − y³ = (x − y)(x² + xy + y²), with x = 5 and y = 3p⁴, gives (5 − 3p⁴)(25 + 15p⁴ + 9p⁸). This is choice A.

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