Factorize:
Question:

Factorize:

$a b\left(x^{2}+y^{2}\right)-x y\left(a^{2}+b^{2}\right)$

 

Solution:

We have:

$a b\left(x^{2}+y^{2}\right)-x y\left(a^{2}+b^{2}\right)=a b x^{2}+a b y^{2}-a^{2} x y-b^{2} x y$

$=\left(a b x^{2}-a^{2} x y\right)-\left(b^{2} x y-a b y^{2}\right)$

$=a x(b x-a y)-b y(b x-a y)$

$=(b x-a y)(a x-b y)$

 

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