Prove that P \[ -\left|\begin{array}{ccc} 1 & a^{2}+b c & a^{3} \\ ...
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0Prove that
P
\[
-\left|\begin{array}{ccc}
1 & a^{2}+b c & a^{3} \\
1 & b^{2}+c a & b^{3} \\
1 & c^{2}+a b & c^{3}
\end{array}\right|=-(a-b)(b-c)(c-a)\left(a^{2}+b^{2}+c^{2}\right)
\]
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