Using properties of determinants, prove that: \[ \left|\begin{array...

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Using properties of determinants, prove that:
\[
\left|\begin{array}{lll}
\alpha & \alpha^{2} & \beta+\gamma \\
\beta & \beta^{2} & \gamma+\alpha \\
\gamma & \gamma^{2} & \alpha+\beta
\end{array}\right|=(\beta-\gamma)(\gamma-\alpha)(\alpha-\beta)(\alpha+\beta+\gamma)
\]
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