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(a + b)^2 Expansion and Visualisation

Factorize: x...

Question

Factorize:
$x^{2} + 4 x y - 4 z^{2} + 4 y^{2}$

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Solution

$x^{2} + 4 x y - 4 z^{2} + 4 y^{2}$
$= x^{2} + 4 x y + 4 y^{2} - 4 z^{2}$
$= x^{2} + 2. x .2 y + (2 y)^{2} - (2 z)^{2}$
$= (x + 2 y)^{2} - (2 z)^{2}$
$= (x + 2 y + 2 z) (x + 2 y - 2 z)$ .

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