Solve: a^4-16(b-c)^2 - Vidyadip

Question

Solve:
$a^4-16(b-c)^2$

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Answer

$a^4-16(b-c)^2$
$= \left(a^2\right)^2-\left[4(b-c)^2\right]^2$
$= {\left[a^2+4(b-c)^2\right]\left[a^2-4(b-c)^2\right] }$
$= {\left[a^2+4(b-c)^2\right]\left[a^2-[2(b-c)]^2\right] }$
$= {\left[a^2+3(b-c)^2\right][a+2(b-c)][a-2(b-c)] }$
$= {\left[a^2+4(b-c)^2\right](a+2 b-2 c)(a-2 b+2 c) }$

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