What are the factors for $128 m - 2 m^{4}$ $128m-2m^4$ ?

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Answer 1 · 2015-05-30T17:24:45

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

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

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

...using the difference of cubes identity

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ $a^3 - b^3 = (a-b)(a^2+ab+b^2)$

There are no simpler factors with real coefficients.

What are the factors for 128m-2m^4128m−2m4128m-2m^4?