Question
Solve:
$ a^4 b^4-16 c^4 $
$ a^4 b^4-16 c^4 $
✓
Answer
$ a^4 b^4-16 c^4 $
$ =\left[\left(a^2 b^2\right)^2-\left(4 c^2\right)^2\right] $
$ =\left(a^2 b^2+4 c^2\right)\left(a^2 b^2-4 c^2\right) $
$ =\left(a^2 b^2+4 c^2\right)\left[(a b)^2-(2 c)^2\right]$
$ =\left(a^2 b^2+4 c^2\right)(a b+2 c)(a b-2 c) $
$ =\left[\left(a^2 b^2\right)^2-\left(4 c^2\right)^2\right] $
$ =\left(a^2 b^2+4 c^2\right)\left(a^2 b^2-4 c^2\right) $
$ =\left(a^2 b^2+4 c^2\right)\left[(a b)^2-(2 c)^2\right]$
$ =\left(a^2 b^2+4 c^2\right)(a b+2 c)(a b-2 c) $
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