Factorize:
Question:

Factorize:

$x(x+y)^{3}-3 x^{2} y(x+y)$

 

Solution:

We have:

$x(x+y)^{3}-3 x^{2} y(x+y)=x(x+y)\left[(x+y)^{2}-3 x y\right]$

$=x(x+y)\left[x^{2}+y^{2}+2 x y-3 x y\right]$

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

 

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