Factors of $x^{4} - 13 x^{2} y^{2} + 36 y^{4}$ are

(x + 4 y) (x - 4 y) (x + 2 y) (x - 2 y)

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(x^{2} + 2 x - 8) (x^{2} + 2 x - 3)

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(x + 3 y) (x - 3 y) (x + 2 y) (x - 2 y)

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None of these

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Solution

The correct option is B $(x + 3 y) (x - 3 y) (x + 2 y) (x - 2 y)$
$x^{4} - 13 x^{2} y^{2} + 36 y^{4}$
$= x^{4} - 9 x^{2} y^{2} - 4 x^{2} y^{2} + 36 y^{4}$
$= x^{2} (x^{2} - 9 y^{2}) - 4 y^{2} (x^{2} - 9 y^{2})$
$= (x^{2} - 9 y^{2}) (x^{2} - 4 y^{2})$
$= (x + 3 y) (x - 3 y) (x + 2 y) (x - 2 y)$

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