Factorize :
$x^{4} + y^{4} - 2 x^{2} y^{2}$

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

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

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

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

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Solution

The correct option is A $(x^{2} - y^{2} - x y) (x^{2} - y^{2} + x y)$
Given, $x^{4} + y^{4} - 2 x^{2} y^{2}$
Using,
$(a - b)^{2} = a^{2} - 2 a b + b^{2}$

$\Rightarrow$ $(x^{2})^{2} + (y^{2})^{2} - 2 (x^{2}) (y^{2}) - x^{2} y^{2}$
$= (x^{2} - y^{2})^{2} - (x y)^{2}$
Using,
$(a^{2} - b^{2}) = (a + b) (a - b)$
$\Rightarrow$ $(x^{2} - y^{2} + x y) (x^{2} - y^{2} - x y)$

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