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