# What are the factors for 128m-2m^4?

May 30, 2015

$128 m - 2 {m}^{4} = 2 m \left({4}^{3} - {m}^{3}\right)$

$= 2 m \left(4 - m\right) \left({4}^{2} + 4 m + {m}^{2}\right)$

$= 2 m \left(4 - m\right) \left(16 + 4 m + {m}^{2}\right)$

...using the difference of cubes identity

${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$

There are no simpler factors with real coefficients.