Question

How would the expression x^3 - 64 be rewritten using difference of cubes? A. (x + 4)(x^2 - 4x + 16) B. (x-4)(x^2 + 4x + 16) C. (x+4)(x^2 - 4x - 16) D. (x-4)(x^2 + 16x+4)​

Answer 1

D)

Explanation:

4 is an evident zero of the equation x^3 - 64.

x^3 - 64 can only be factorized with (x-4) and not with (x+4)

because x - 4 = 0 <==> x = 4 and 4^3 -64 = 0

Developing B) would be:

x^3 + 4x^3 + 16x - 4x^2 - 16x - 64 = 5x^3 - 4x^2 -64

So it doesn't match so it's D)