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Factorize:$a^2 + 4b^2 – 4ab – 4c^2$
Given :
$a^2 + 4b^2 – 4ab – 4c^2$
To do :
We have to factorize the given expression.
Solution :
$a^{2}+4 b^{2}-4 a b-4 c^{2}=(a)^{2}+(2 b)^{2}-2 \times a \times 2 b-(2 c)^{2}$
$=(a-2 b)^{2}-(2 c)^{2}$ [Since $(a-b)^2=a^2+b^2-2ab$]
$=(a-2 b+2 c)(a-2 b-2 c)$ [Since $a^2-b^2=(a+b)(a-b)$]
Hence, $a^{2}+4 b^{2}-4 a b-4 c^{2}=(a-2 b+2 c)(a-2 b-2 c)$.
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