Using properties of determinants, prove the identities: \[ \left|\begin{array}{lll} y+z & x+y & ...

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Using properties of determinants, prove the identities:
\[
\left|\begin{array}{lll}
y+z & x+y & x \\
z+x & y+z & y \\
x+y & z+x & z
\end{array}\right|=x^{3}+y^{3}+z^{3}-3 x y z
\]
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