Without expanding, show that the value of each of the following determinants is zero \[ \left|\b...

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Without expanding, show that the value of each of the following determinants is zero
\[
\left|\begin{array}{lll}
1 & a & a^{2}-b c \\
1 & b & b^{2}-a c \\
1 & c & c^{2}-a b
\end{array}\right|
\]
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