Show that

$\displaystyle

\left| {\begin{array}{*{20}c}

{n^2 } & {(n + 1)^2 } & {(n + 2)^2 } \\

{(n + 1)^2 } & {(n + 2)^2 } & {(n + 3)^2 } \\

{(n + 2)^2 } & {(n + 3)^2 } & {(n + 4)^2 } \\

\end{array}} \right| = - 8

$

I know that I can useSarrusbut I think I will get a complicated equation. Is there any other ways to solve this ?

thanks