$(a - b)^{4} + (a + b)^{4}$

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Solution

$\begin{matrix} {(a - b)}^{4} + {(a + b)}^{4} = [{(a - b)}^{2} + {(a + b)}^{2}] [(a - b) + (a - b)] [(a + b) - (a - b)] = [{(a - b)}^{2} + {(a - b)}^{2}] [(2 a) (2 b)] = 4 a b [{(a - b)}^{2} + {(a + b)}^{2}] \end{matrix}$

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