Question

How do you factor `(x- 4)^3 -27`?

Answer 1

`(x-4)^3-3^3=((x-4)-3)((x-4)^2+3(x-4)+9)=(x-7)(x^2-8x+16+3x-12+9)=(x-7)(x^2-5x+13)`

Explanation:

This is a difference of 2 cubes so to factor use the formula `x^3-y^3=(x-y)(x^2+xy+y^2)` and then simplify