Prove the identities: ` |{:(b^(2)+c^(2),,ab,,ac),(ab,,c^(2)+a^(2),,bc),(ca,,bc,,a^(2)+b^(2)):}|=4a^2b^2c^2`

Explanation

To prove the identity

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