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Using properties of determinants prove that:
\[
\left|\begin{array}{ccc}
(m+n)^{2} & l^{2} & m n \\
(n+l)^{2} & m^{2} & l n \\
(l+m)^{2} & n^{2} & l m
\end{array}\right|=\left(l^{2}+m^{2}+n^{2}\right)(l-m)(m-n)(n-l)
\]
\( \mathrm{P} \)
W
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