Question:
Factorize each of the following expression:
a4 − (2b + c)4
Solution:
$a^{4}-(2 b+c)^{4}$
$=\left(a^{2}\right)^{2}-\left[(2 b+c)^{2}\right]^{2}$
$=\left[a^{2}+(2 b+c)^{2}\right]\left[a^{2}-(2 b+c)^{2}\right]$
$=\left[a^{2}+(2 b+c)^{2}\right]\{[a+(2 b+c)][a-(2 b+c)]\}$
$=\left[a^{2}+(2 b+c)^{2}\right](a+2 b+c)(a-2 b-c)$
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