Prove that \[ \left|\begin{array}{ccc} a & b-c & c+b \\ a+c & b & c...

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