Prove the identities: `|[a^2,a^2-(b-c)^2,b c], [b^2,b^2-(c-a)^2,c a],[ c^2,c^2-(a-b)^2,a b]|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)`

Explanation

$$
\Delta=\left|\begin{array}{lll}
a^{2} & a^{2}-(b-c)^{2} & b c \\
b^{2} & b^{2}-(c-a)^{2} & c a \\
c^{2} & c^{2}-(a-b)^{2} & a b
\end{array}\right|=\left|\begin{array}{ccc}
a^{2} & a^{2} & b c \\
b^{2} & b^{2} & c a \\
...