Using properties of determinants prove that: P If \( x \neq y \neq ...

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Using properties of determinants prove that:
P If \( x \neq y \neq z \) and \( \left|\begin{array}{ccc}x & x^{3} & x^{4}-1 \\ y & y^{3} & y^{4}-1 \\ z & z^{3} & z^{4}-1\end{array}\right|=0 \), prove that \( x y z(x y+y z+z x)=(x+y+z) \)
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