Factorise: $x^{3} y^{6} - 64$ .

(x y^{2} + 4) (x^{2} y^{4} + 4 x y^{2} + 16)

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(x y^{2} - 4) (x^{2} y^{4} - 4 x y^{2} + 16)

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(x y^{2} - 4) (x^{2} y^{4} + 4 x y^{2} + 16)

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(x y^{2} + 4) (x^{2} y^{4} - 4 x y^{2} + 16)

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Solution

The correct option is C $(x y^{2} - 4) (x^{2} y^{4} + 4 x y^{2} + 16)$
Using the identity:
$a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)$
$x^{3} y^{6} - 64 = (x y^{2})^{3} - 4^{3} = (x y^{2} - 1) (x^{2} y^{4} + 16 + 4 x y^{2})$

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