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.