Factorise

Question:

Factorise

$x^{4} y^{4}-x y$

 

Solution:

Using the identity 

$a^{3}-b^{3}=(a-b)\left(a^{2}+b^{2}+a b\right)$

$x^{4} y^{4}-x y=x y\left(x^{3} y^{3}-1\right)$

$=x y(x y-1)\left(x^{2} y^{2}+1+x y\right)$

 

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