Factorise
a¹² – b¹²

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Solution

a¹² – b^{12

$= (a^{6} + b^{6}) (a^{6} - b^{6}) = [{(a^{2})}^{3} + {(b^{2})}^{3}] [{(a^{3})}^{2} - {(b^{3})}^{2}] = [(a^{2} + b^{2}) (a^{4} + b^{4} - a^{2} b^{2})] [(a^{3} - b^{3}) (a^{3} + b^{3})] = [(a^{2} + b^{2}) (a^{4} + b^{4} - a^{2} b^{2})] [(a - b) (a^{2} + b^{2} + a b) (a + b) (a^{2} + b^{2} - a b)] = (a - b) (a^{2} + b^{2} + a b) (a + b) (a^{2} + b^{2} - a b) (a^{2} + b^{2}) (a^{4} + b^{4} - a^{2} b^{2})$}

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