What is the factorization of 216x12 - 64?

A. (6x3 - 4) (36x6 + 24x3 + 16)

B. (6x3 - 4) (36x9 + 24x3 + 16)

C. (6x4 - 4) (36x8 + 24x4 + 16)

D. (6x4 - 4) (36x12 + 24x4 + 16)

This is a difference of cubes of the form:

(a^3-b^3) which always factors to (a-b) (a^2+ab+b^2)

So if you find the cube of each term you will have a and b for the factors above.

(216x^12) ^ (1/3) = 6x^4 and 64^ (1/3) = 4 so

(6x^4-4) (36x^8+24x^4+16), So C. is the correct answer.