Question

Use polynomial identities to factor 64 + 27a3.
Responses

A. (4 – 3a)(16 – 12a + 9a2)
A. (4 – 3 a )(16 – 12 a + 9 a 2 )

B. (4 + 3a)(16 + 12a + 9a2)
B. (4 + 3 a )(16 + 12 a + 9 a 2 )

C. (4 + 3a)(16 – 12a + 9a2)
C. (4 + 3 a )(16 – 12 a + 9 a 2 )

D. (4 + 3a)3

Answer 1

64 + 27a^3 = 4^3 + (3a)^3, a sum of cubes. Using x^3 + y^3 = (x + y)(x^2 - xy + y^2) with x = 4, y = 3a gives

(4 + 3a)(16 - 12a + 9a^2).

So the correct choice is C.