Factorise
$a^{2} + 4 b^{2} - 4 a b - 4 c^{2}$ .

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Solution

$a^{2} + {(2 b)}^{2} - 2 (2 b) (a) - {(2 c)}^{2}$
using $x^{2} + y^{2} - 2 x y = {(x - y)}^{2}$ we get ,
${(a - 2 b)}^{2} - {(2 c)}^{2}$
using $x^{2} - y^{2} = (x + y) (x - y)$ , we get
$(a - 2 b + 2 c) . (a - 2 b - 2 c)$

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