$n^{3}\left ( n^{2} - 7 \right )^{2} - 36n$
$= n\left [n^{2}\left ( n^{2} - 7 \right )^{2} - 36 \right ]$
$= n\left [ \left ( n^{3} - 7n \right )^{2} - 36 \right ]$
$= n\left ( n^{3} - 7n - 6 \right )\left ( n^{3} - 7n + 6 \right )$
$= n\left ( n^{3} + n^{2} - n^{2} - n - 6n - 6 \right )\left ( n^{3} - n^{2} + n^{2} - n - 6n + 6 \right )$
$= n\left [ n^{2}\left ( n + 1 \right ) - n\left ( n + 1 \right ) - 6\left ( n + 1 \right ) \right ].\left [ n^{2}\left ( n - 1 \right ) + n\left ( n - 1 \right ) - 6\left ( n - 1 \right ) \right ]$
$= n\left ( n + 1 \right )\left ( n^{2} - n + 6 \right )\left ( n - 1 \right )\left ( n^{2} + n - 6 \right )$
$= n\left ( n + 1 \right )\left ( n^{2} + 2n - 3n + 6 \right )\left ( n - 1 \right )\left ( n^{2} + 3n - 2n - 6 \right )$
$= n\left ( n + 1 \right ).\left [ n\left ( n + 2 \right ) - 3\left ( n + 2 \right ) \right ].\left ( n - 1 \right ).\left [ n\left ( n + 3 \right ) - 3\left ( n + 3 \right ) \right ]$
$= n\left ( n + 1 \right )\left ( n + 2 \right )\left ( n - 3 \right )\left ( n - 1 \right )\left ( n + 3 \right )\left ( n - 2 \right )$
$= n\left ( n^{2} - 1 \right )\left ( n^{2} - 4 \right )\left ( n^{2} - 9 \right )$
