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Expansion of (x^2 - y^2)

Factorize:𝑎2...

Question

Factorize:
$a^{2} + 4 b^{2} - 4 a b - 4 c^{2}$

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Solution

Given: $a^{2} + 4 b^{2} - 4 a b - 4 c^{2}$
$∴ a^{2} + 4 b^{2} - 4 a b - 4 c^{2}$
$= (a - 2 b)^{2} - 4 c^{2}$
$[∵ x^{2} + y^{2} - 2 x y = (x - y)^{2}]$
$= (a - 2 b)^{2} - (2 c)^{2}$
$= (a - 2 b + 2 c) (a - 2 b - 2 c)$
$[∵ x^{2} - y^{2} = (x + y) (x - y)]$

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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Expansion of (x^2 - y^2)

Standard VIII Mathematics

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