How do I Factor 125x^3 - 64

The answer is not (5x+4) (5x-4) or (5x-4) (25x^2 + 15x+16)

The correct factorization would be (5x - 4) (25x^2 + 20x + 16).

The law of factoring cubes states that we use the following formula when we have two cubes being subtracted by one another.

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

If we take the cube root of 125x^3 we get 5x, which will be our a value. If we take the cube root of 64, we get 4, which will be our b value. Then we plug in to the formula.

(5x - 4) ((5x) ^2 + (5x) (4) + 4^2)

(5x - 4) (25x^2 + 20x + 16)

I think the problem with your second answer is that you just did not properly multiply the 5x and the 4 to get 20x (instead you got 15x).