The factors of $x^{4} + y^{4} + x^{2} y^{2}$ are:

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

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

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

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Factorization is not possible

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Solution

The correct option is C $(x^{2} + y^{2} + x y) (x^{2} + y^{2} - x y)$
Let us solve $x^{4} + y^{4} + x^{2} y^{2}$
$= (x^{4} + y^{4} + 2 x^{2} y^{2}) - x^{2} y^{2}$
$= (x^{2} + y^{2})^{2} - (x y)^{2}$
Using $a^{2} - b^{2} = (a + b) (a - b)$
$x^{4} + y^{4} + x^{2} y^{2} = (x^{2} + y^{2} + x y) (x^{2} + y^{2} - x y)$
Hence, option C is correct

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