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Using properties of determinants prove that:
\( \mathrm{P} \)
\[
\left|\begin{array}{ccc}
-a\left(b^{2}+c^{2}-a^{2}\right) & 2 b^{3} & 2 c^{3} \\
2 a^{3} & -b\left(c^{2}+a^{2}-b^{2}\right) & 2 c^{3} \\
2 a^{3} & 2 b^{3} & -c\left(a^{2}+b^{2}-c^{2}\right)
\end{array}\right|=(a b c)\left(a^{2}+b^{2}+c^{2}\right)^{3}
\]
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