How do you factor $256n^4-c^4$ ?

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Answer 1 · 2017-02-05T17:22:30

$256n^4-c^4=(16n^2+c^2)(4n+c)(4n-c)$

As the two monomials $256n^4$ and $c^4$ are perfect square,

we can use the identity $a^2-b^2=(a+b)(a-b)$ to factorize it and

$256n^4-c^4$

= $(16n^2)^2-(c^2)^2$

= $(16n^2+c^2)(16n^2-c^2)$

= $(16n^2+c^2)((4n)^2-c^2)$

= $(16n^2+c^2)(4n+c)(4n-c)$

How do you factor 256n^4-c^4256n^4-c^4?