Factorize each of the following expression:

$a^{4}-16(b-c)^{4}$

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

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

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

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

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