$x^{12} - y^{12}$ is equal to ?

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Solution

Simplify using algebraic identities
$x^{12} - y^{12} = {(x^{6})}^{2} - {(y^{6})}^{2} = (x^{6} - y^{6}) (x^{6} + y^{6}) [∵ a^{2} - b^{2} = (a - b) (a + b)] = ({(x^{3})}^{2} - {(y^{3})}^{2}) (x^{6} + y^{6}) = (x^{3} - y^{3}) (x^{3} + y^{3}) (x^{6} + y^{6}) [∵ a^{2} - b^{2} = (a - b) (a + b)] = (x^{3} - y^{3}) (x^{3} + y^{3}) (x^{6} + y^{6}) = (x - y) (x^{2} + y^{2} + x y) (x^{3} + y^{3}) (x^{6} + y^{6}) [∵ a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)]$
Thus, $(x^{12} - y^{12}) = (x - y) (x^{2} + y^{2} + x y) (x^{3} + y^{3}) (x^{6} + y^{6})$

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$x^{12} - y^{12}$ is equal to ?