If \( a, b, c \in \mathbf{R}, d=a+b+c \), and \[ \Delta=\left|\begi...

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If \( a, b, c \in \mathbf{R}, d=a+b+c \), and
\[
\Delta=\left|\begin{array}{lll}
a & d & d \\
d & b & d \\
d & d & c
\end{array}\right|
\]
then \( \Delta \) equals
(a) \( a^{3} b^{3} c^{3} \)
(b) \( a^{3}+b^{3}+c^{3} \)
(c) \( d^{3} \)
(d) none of these.
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