Factorise the following:
$x^{4} - 8 x^{2} y^{2} + 12 y^{4}$

(x^{2} + 6 y^{2}) (x^{3} - 2 y^{2})

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(x^{2} - 6 y^{2}) (x^{3} - 2 y^{2})

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(x^{2} - 6 y^{2}) (x^{2} - 2 y^{2})

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(x^{2} + 6 y^{2}) (x^{2} + 2 y^{2})

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Solution

The correct option is D $(x^{2} - 6 y^{2}) (x^{2} - 2 y^{2})$
$x^{4} - 8 x^{2} y^{2} + 12 y^{4}$
$= x^{4} - 6 x^{2} y^{2} - 2 x^{2} y^{2} + 12 y^{4}$
$= x^{2} (x^{2} - 6 y^{2}) - 2 y^{2} (x^{2} - 6 y^{2})$
$= (x^{2} - 6 y^{2}) (x^{2} - 2 y^{2})$

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