[tex] \rm prove \: \: \: \: that \: \: \: \text{:- } \left|\begin{array}{ccc} \rm3 a & \rm -a+b &\rm -a+c \\\rm -b+a & \rm3 b &\rm -b+c \\ \rm-c+a & \rm-c+b & \rm3 c\end{array}\right|=3(a+b+c)(a b+b c+c a)[/tex]


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[tex] \rule{300pt}{0.1pt}[/tex]

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