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 $(x^{2} + y^{2} + x y) (x^{2} + y^{2} - x y)$
Given : x⁴ + x²y² + y⁴
= (x⁴ + 2x²y² + y⁴) - x²y²
= (x² + y²)² – (xy)²
= [(x² + y²) + xy] [(x² + y²) – xy]
= (x² + xy + y²)(x² –xy + y²)

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