LCM of the polyonomials $x^{3} y - x y^{3}, x^{4} - 2 x^{2} y^{2} + y^{4}$ and $x^{4} - y^{4}$ is

x y (x^{2} - y^{2}) (x + y)^{2} (x - y)

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x y (x^{2} + y^{2}) (x - y)^{2} {(x + y)}^{2}

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x y (x^{2} + y^{2}) (x - y)^{2} (x + y)

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x y (x^{2} - y^{2}) (x - y) (x + y)

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Solution

The correct option is B $x y (x^{2} + y^{2}) (x - y)^{2} {(x + y)}^{2}$
$x^{3} y - x y^{3} = x y (x - y) (x + y)$
$x^{4} - 2 x^{2} y^{2} + y^{4} = {(x^{2} - y^{2})}^{2}$
$= {(x - y)}^{2} {(x + y)}^{2}$
$x^{4} - y^{4} = (x - y) (x + y) (x^{2} + y^{2})$
$∴ L . C . M . = x y (x - y)^{2} (x + y)^{2} (x^{2} + y^{2})$

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