Factorize:
$(3 x + y)^{2} (4 x - 5) + x y (3 x + y)^{2} (4 x - 5) (x + 2 y)$

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Solution

We have,

Let $A = (3 x + y)^{2} (4 x - 5) + x y (3 x + y)^{2} (4 x - 5) (x + 2 y)$

According to the question,
$= (3 x + y)^{2} (4 x - 5) + x y (3 x + y)^{2} (4 x - 5) (x + 2 y)$

$= (3 x + y)^{2} (4 x - 5) [1 + x y (x + 2 y)]$

$A = (3 x + y)^{2} (4 x - 5) [1 + x^{2} y + 2 x y^{2}]$

Hence, this is the answer.

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