Sum and difference of cubes question! 10 pts for best answer!! im not asking for answer i promise:)?

I think you did a typo and it's supposed to be 27x^3 - 125, since 2 isn't a perfect cube. Anyway, you got the three in front of the x because the cube root of 27x^3 is 3x. Likewise, the cube root of 125 is 5. To factor a difference of two cubes it's always a^3 - b^3 = (a - b)(a^2 + ab + b^2), where a is the cube root of the first term. That's where you got it.