Factorize the following:


Factorize the following:
x4y2 − x2y4 − x4y4


The greatest common factor of the terms $x^{4} y^{2}, x^{2} y^{4}$ and $x^{4} y^{4}$ of the expression $x^{4} y^{2}-x^{2} y^{4}-x^{4} y^{4}$ is $x^{2} y^{2}$.

Also, we can write $x^{4} y^{2}=x^{2} y^{2} \times x^{2}, x^{2} y^{4}=x^{2} y^{2} \times y^{2}$ and $x^{4} y^{4}=x^{2} y^{2} \times x^{2} y^{2}$.

$\therefore x^{4} y^{2}-x^{2} y^{4}-x^{4} y^{4}=x^{2} y^{2} \times x^{2}-x^{2} y^{2} \times y^{2}-x^{2} y^{2} \times x^{2} y^{2}$

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

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