Factorize:
$x^{4} + x^{2} y^{2} + y^{4}$

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Solution

$\begin{matrix} x^{4} + x^{2} y^{2} + y^{4} & = (x^{2})^{2} + (y^{2})^{2} + x^{2} y^{2} = (x^{2} + y^{2})^{2} - 2 x^{2} y^{2} + x^{2} y^{2} = (x^{2} + y^{2})^{2} - (x y)^{2} = (x^{2} + y^{2} - x y) (x^{2} + y^{2} + x y) \end{matrix}$

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x^{4} + y^{4} + x^{2} y^{2}

x^{4} + y^{4} + x^{2} y^{2}

x^{4} + y^{4} + x^{2} y^{2}

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x^{4} + x^{2} y^{2} + y^{4} = 133

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