Prove that `|{:(a^(2), a^(2)-(b-c)^(2), bc), (b^(2), b^(2)-(c-a)^(2), ca), (c^(2), c^(2)-(a-b)^(2), ab):}|= (a^(2)+b^(2)+c^(2))(a-b)(b-c)(c-a)(a+b+c)`

Explanation

To prove that

\[
\left| \begin{array}{ccc}
a^2 & a^2 - (b - c)^2 & bc \\
b^2 & b^2 - (c - a)^2 & ca \\
c^2 & c^2 - (a - b)^2 & ab
\end{array} \right| = (a^2 + b^2 + c^2)(a - b)(b - c)(c - a)(a + b + c)
...