Factorize:$4(x - y)^2 - 12(x -y) (x + y) + 9(x + y)^2$

Given :

$4(x - y)^2 - 12(x -y) (x + y) + 9(x + y)^2$

To do :

We have to factorize the given expression.

Solution :

$4(x - y)^2 - 12(x - y) (x + y) + 9(x + y)^2 = [2(x - y)]^2 + 2 \times 2(x - y) \times 3(x + y) + [3 (x+y)]^2$

$= [2(x - y) + 3(x + y)]^2$

$= (2x-2y + 3x + 3y)^2$

$= (5x + y)^2$

Hence, $4(x - y)^2 - 12(x - y) (x + y) + 9(x + y)^2 = (5x + y)^2$.

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Updated on: 10-Oct-2022

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