Using properties of determinants prove that:
P
\[
\left|\begin{arra...
Using properties of determinants prove that:
P
\[
\left|\begin{array}{ccc}
x & y & z \\
x^{2} & y^{2} & z^{2} \\
x^{3} & y^{3} & z^{3}
\end{array}\right|=x y z(x-y)(y-z)(z-x) .
\]
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