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