Factorise the following:
$2 x^{4} - 13 x^{2} y^{2} + 15 y^{4}$

(x^{2} - 5 y^{2}) (2 x^{2} - 3 y^{2})

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(x^{3} - 5 y^{3}) (2 x^{3} - 3 y^{2})

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(x^{2} - 5 y^{2}) (2 x^{3} - 3 x y^{2})

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(x^{3} - 5 y^{3}) (2 x^{2} - 3 x y^{2})

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Solution

The correct option is A $(x^{2} - 5 y^{2}) (2 x^{2} - 3 y^{2})$
$2 x^{4} - 13 x^{2} y^{2} + 15 y^{4}$
$= 2 x^{4} - 10 x^{2} y^{2} - 3 x^{2} y^{2} + 15 y^{4}$
$= 2 x^{2} (x^{2} - 5 y^{2}) - 3 y^{2} (x^{2} - 5 y^{2})$
$= (x^{2} - 5 y^{2}) (2 x^{2} - 3 y^{2})$

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x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 8

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(x^{2} y - 3 y^{2} + 5 x y^{2}) - (- x^{2} y + 3 x y^{2} - 3 y^{2})

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