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