Prove that `|[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c^2`

Explanation

To prove that

\[
\left| \begin{array}{ccc}
a^2 & bc & ac + c^2 \\
a^2 + ab & b^2 & ac \\
ab & b^2 + bc & c^2
\end{array} \right| = 4a^2b^2c^2,
...