Question:
Factorize each of the following expression:
a4 − 16(b − c)4
Solution:
$a^{4}-16(b-c)^{4}$
$=\left(a^{2}\right)^{2}-\left[4(b-c)^{2}\right]^{2}$
$=\left[a^{2}+4(b-c)^{2}\right]\left[a^{2}-4(b-c)^{2}\right]$
$=\left[a^{2}+4(b-c)^{2}\right]\left\{a^{2}-[2(b-c)]^{2}\right\}$
$=\left[a^{2}+4(b-c)^{2}\right][a+2(b-c)][a-2(b-c)]$
$=\left[a^{2}+4(b-c)^{2}\right](a+2 b-2 c)(a-2 b+2 c)$
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