Using properties of determinants, prove that `|[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)`

Explanation

To prove that

\[
\left| \begin{array}{ccc}
a+x & y & z \\
x & a+y & z \\
x & y & a+z
\end{array} \right| = a^2(a+x+y+z),
...