Expand: $(n - 1) (n + 1) (n^{2} + 1)$

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Solution

As we know the formula $(a + b) (a - b)$ = $a^{2} + b^{2}$
So $(n - 1) (n + 1)$ = $n^{2} - 1^{2}$
Substituing the value of $(n - 1) (n + 1)$ = $n^{2} - 1^{2}$ in $(n - 1) (n + 1) (n^{2} + 1)$ we get:
$(n - 1) (n + 1) (n^{2} + 1) = (n^{2} - 1) (n^{2} + 1)$
$= (n^{2})^{2} - (1)^{2}$ Using: [ $(a + b) (a - b)$ = $a^{2} + b^{2}$ ]
Hence, $(n - 1) (n + 1) (n^{2} + 1) = (n^{4} - 1)$

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