Prove that \( \left|\begin{array}{lll}b+c & a-b & a \\ c+a & b-c & b \\ a+b & c-a & c\end{array}...

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Prove that \( \left|\begin{array}{lll}b+c & a-b & a \\ c+a & b-c & b \\ a+b & c-a & c\end{array}\right|=3 a b c-a^{3}-b^{3}-c^{3} \)
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