X^3y^3+1 = (xy)^3 + (1)^3 = (xy +1) [(xy)^2 xy × 1 + (1)^2] = (xy+1) (x^2y^2 xy +1) = (xy +1) (x^2y^2 xy +1) ...

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Algebraic Identities

Factorize x3y...

Question

Factorize $x^{3} y^{3} + 1$

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Solution

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

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