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Factorisation Using Algebraic Identities

Factorize x4y...

Question

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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