Factorise: $1 + n^{4} + n^{8}$

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Solution

$1 + n^{4} + n^{8}$
$= 1 + 2 n^{4} + n^{8} - n^{4}$
$= (1 + n^{4})^{2} - {(n^{2})}^{2}$
$= (1 + n^{4} - n^{2}) (1 + n^{4} + n^{2})$

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