(d) $\left| {\,\begin{array}{*{20}{c}}{b + c}& a & a\\b& {c + a}& b\\c& c& {a + b}\end{array}\,} \right|\, $
$= \,\left| {\,\begin{array}{*{20}{c}}0& { - 2c}& { - 2b}\\b& {c + a}& b\\c& c& {a + b}\end{array}\,} \right|$
$\{$by ${R_1} \to {R_1} - ({R_2} + {R_3})\} $
$= 2c b(a + b - c)\, - 2b.c(b - c - a)\, = 4abc$