Show that \( \left|\begin{array}{lll}{ }^{x} C_{r} & { }^{x} C_{r+1} & { }^{x} C_{r+2} \\ { }^{y...
Show that \( \left|\begin{array}{lll}{ }^{x} C_{r} & { }^{x} C_{r+1} & { }^{x} C_{r+2} \\ { }^{y} C_{r} & { }^{y} C_{r+1} & { }^{y} C_{r+2} \\ { }^{z} C_{r} & { }^{z} C_{r+1} & { }^{z} C_{r+2}\end{array}\right|= \)
\[
\left|\begin{array}{lll}
{ }^{x} C_{r} & { }^{x+1} C_{r+1} & { }^{x+2} C_{r+2} \\
{ }^{y} C_{r} & { }^{y+1} C_{r+1} & { }^{y+2} C_{r+2} \\
{ }^{z} C_{r} & { }^{z+1} C_{r+1} & { }^{z+2} C_{r+2}
\end{array}\right|
\]
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