Determinant of a particular matrix. What is the best way to find determinant of the following matrix?
$$A=\left(\begin{matrix}
1&ax&a^2+x^2\\1&ay&a^2+y^2\\ 1&az&a^2+z^2
\end{matrix}\right)$$
I thought it looks like a Vandermonde matrix, but not exactly. I can't use  $|A+B|=|A|+|B|$ to form a Vandermonde matrix. Please suggest. Thanks.

Note that
$$
\det\left(\begin{matrix}
1&ax&a^2+x^2\\1&ay&a^2+y^2\\ 1&az&a^2+z^2
\end{matrix}\right) =\det \left(\begin{matrix}
1&ax&x^2\\1&ay&y^2\\ 1&az&z^2
\end{matrix}\right)=a\cdot\det \left(\begin{matrix}
1&x&x^2\\1&y&y^2\\ 1&z&z^2
\end{matrix}\right)
$$ which boils down to Vandermonde determinant
$$
a(x-y)(y-z)(z-x).
$$
