Simplify: $(x - y) (x + y) (x^{2} + y^{2}) (x^{4} + y^{4})$

x^{8} - y^{8}

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x^{4} - y^{4}

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x^{8} - y^{8}

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x^{4} + y^{2}

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Solution

The correct option is A $x^{8} - y^{8}$
$(x - y) (x + y) (x^{2} + y^{2}) (x^{4} + y^{4}) = (x^{2} - y^{2}) (x^{2} + y^{2}) (x^{4} + y^{4}) = [(x^{2})^{2} - (y^{2})^{2}] (x^{4} + y^{4}) = (x^{4} - y^{4}) (x^{4} + y^{4}) = (x^{4})^{2} - (y^{4})^{2} = x^{8} - y^{8}$

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