Question:
Factorize each of the following algebraic expression:
a2 + 4b2 − 4ab − 4c2
Solution:
$a^{2}+4 b^{2}-4 a b-4 c^{2}$
$=\left(a^{2}-4 a b+4 b^{2}\right)-4 c^{2}$
$=\left[a^{2}-2 \times a \times 2 b+(2 b)^{2}\right]-4 c^{2}$
$=(a-2 b)^{2}-(2 c)^{2}$
$=[(a-2 b)-2 c][(a-2 b)+2 c]$
$=(a-2 b-2 c)(a-2 b+2 c)$
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