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Without expanding the determinant, prove that:
\[
\left|\begin{array}{lll}
1 & a & a^{2} \\
1 & b & b^{2} \\
1 & c & c^{2}
\end{array}\right|=\left|\begin{array}{ccc}
1 & b c & b+c \\
1 & c a & c+a \\
1 & a b & a+b
\end{array}\right|
\]
\( \mathrm{P} \)
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