(c) $\left| {\,\begin{array}{*{20}{c}}1&1&1\\{bc}&{ca}&{ab}\\{b + c}&{c + a}&{a + b}\end{array}\,} \right|$ = $\left| {\,\begin{array}{*{20}{c}}0&0&1\\{c(b - a)}&{a(c - b)}&{ab}\\{b - a}&{c + a}&{a + b}\end{array}\,} \right|$
$\{ {C_1} \to {C_1} - {C_2},\,{C_2} \to {C_2} - {C_3}\} $
= $(b - a)\,\,(c - b)\,\,\left| {\,\begin{array}{*{20}{c}}0&0&1\\c&a&{ab}\\1&1&{a + b}\end{array}\,} \right|$= $(b - a)\,(c - a)\,\,(c - a)$
$ = (a - b)\,\,(b - c)\,\,(c - a)$.