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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