# How do you factor 3x^4 y - 24xy^4?

$3 {x}^{4} y - 24 x {y}^{4} = 3 x y \left({x}^{3} - 8 {y}^{3}\right)$
We're not finished because 8 is a cube, so $8 {y}^{3} = {\left(2 y\right)}^{3}$ and we can factor the difference of cubes: ${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$
$3 {x}^{4} y - 24 x {y}^{4} = 3 x y \left({x}^{3} - 8 {y}^{3}\right) = 3 x y \left(x - 2 y\right) \left({x}^{2} + 2 x y + 4 {y}^{2}\right)$