\left |\begin{array}{ccc}
ax & a^2+x^2 & 1\\
ay & a^2+y^2 & 1\\
az & a^2+z^2 & 1\\
\end{array}\right |=a\left |\begin{array}{ccc}
x & a^2+x^2 & 1\\
y & a^2+y^2 & 1\\
z & a^2+z^2 & 1\\
\end{array}\right |=a\left |\begin{array}{ccc}
x & x^2 & 1\\
y & y^2 & 1\\
z & z^2 & 1\\
\end{array}\right |=a\left |\begin{array}{ccc}
1 & x & x^2\\
1 & y & y^2\\
1 & z & z^2\\
\end{array}\right |