Factorise
$a^{6} + b^{6}$

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Solution

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

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