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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Updated on: 10-Oct-2022

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