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

${\left(x - 4\right)}^{3} - {3}^{3} = \left(\left(x - 4\right) - 3\right) \left({\left(x - 4\right)}^{2} + 3 \left(x - 4\right) + 9\right) = \left(x - 7\right) \left({x}^{2} - 8 x + 16 + 3 x - 12 + 9\right) = \left(x - 7\right) \left({x}^{2} - 5 x + 13\right)$
This is a difference of 2 cubes so to factor use the formula ${x}^{3} - {y}^{3} = \left(x - y\right) \left({x}^{2} + x y + {y}^{2}\right)$ and then simplify