LCM of the polynomials $x^{3} y - x y^{3}, x^{4} - 2 x^{2} y^{2} + y^{4}$ 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 $x y (x^{2} + y^{2}) (x - y)^{2} (x + y)^{2}$
$x^{3} y - x y^{3} = x y (x^{2} - y^{2})$
$x^{4} - 2 x^{2} y^{2} + y^{4} = (x^{2} - y^{2})^{2}$
$x^{4} - y^{4} = (x^{2} + y^{2}) (x^{2} - y^{2})$
Hence, LCM is : $x y (x^{2} + y^{2}) (x^{2} - y^{2})^{2}$ = $x y (x^{2} + y^{2}) (x - y)^{2} (x + y)^{2}$

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