Factorize:

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

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Solution

$x^{4} + x^{2} y^{2} + y^{4} = (x^{2})^{2} + 2 x^{2} y^{2} + y^{4} - x^{2} y^{2} = (x^{2} + y^{2})^{2} - (x y)^{2} {∵ a^{2} - b^{2} = (a + b) (a - b)} = (x^{2} + y^{2} + x y) (x^{2} + y^{2} - x y) = (x^{2} + x y + y^{2}) (x^{2} - x y + y^{2})$

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121

Similar questions

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

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

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

x^{2} - x y + y^{2} = 7

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

x^{4} + x^{2} y^{2} + y^{4} = 931

x^{2} - x y + y^{2} = 19

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