How would the expression x3 - 64 be rewritten using difference of cubes? A. (x + 4) (x2 - 4x - 16) B. (x - 4) (x2 + 4x + 16) C. (x + 4) (x2 - 4x + 16) D. (x - 4) (x2 + 16x + 4)

B. (x - 4) (x2 + 4x + 16)

Step-by-step explanation:

a3 - b3 = (a - b) (a2 + ab + b2)

substitute a=x n b=4 (cuz 64=4x4x4)

x3 - 64 = (x-4) (x2+4x+4x4)

= (x - 4) (x2 + 4x + 16)

B. (x - 4) (x2 + 4x + 16)

Step-by-step explanation:

Difference of cubes can be rewritten as:

a^3 - b^3 = (a - b) (a^2 + ab + b^2)

So in this case, x^3 - 64 = x^3 - (4) ^3 where a = x and b = 4

= (x-4) (x^2 + 4x + 4^2)

= (x-4) (x^2 + 4x + 16)

The answer is B.