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

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Solution

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

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

x^{2} + x y + x y + y^{2}

x^{3} y^{2}, x^{2} y^{3}

x^{4} y^{4}

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