Solve: a^4-(2 b+c)^4 - Vidyadip

Question

Solve:
$ a^4-(2 b+c)^4 $

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Answer

$ a^4-(2 b+c)^4 $
$ =\left(a^2\right)^2-\left[(2 b+c)^2\right]^2 $
$ =\left[a^2+(2 b+c)^2\right]\left[a^2-(2 b+c)^2\right] $
$ =\left[a^2+(2 b+c)^2\right]\{[a+(2 b+c)][a-(2 b+c)]\} $
$ =\left[a^2+(2 b+c)^2\right](a+2 b+c)(a-2 b-c) $

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