Prove that: `|{:(-2a,, a+b,, a+c), (b+a,,-2b,,b+c),(c+a ,,c+b,,-2c):}|=4(a+b)(b+c)(c+a)`

Explanation

To prove that

\[
\left| \begin{array}{ccc}
-2a & a+b & a+c \\
b+a & -2b & b+c \\
c+a & c+b & -2c
\end{array} \right| = 4(a+b)(b+c)(c+a),
...