The expressions $a+bc$ and $(a+b)(a+c)$ are: 
$\textbf{(A)}\ \text{always equal}\qquad\textbf{(B)}\ \text{never equal}\qquad\textbf{(C)}\ \text{equal whenever }a+b+c=1\\ \textbf{(D)}\ \text{equal when }a+b+c=0\qquad\textbf{(E)}\ \text{equal only when }a=b=c=0$
Using the FOIL method, we see that $(a+b)(a+c) = a^2 + ab + ac + bc.$ We want to solve 
\[a + bc = a^2 + ab + ac + bc\]
\[a = a^2 + ab + ac\]
\[a((a + b + c) - 1) = 0\]
These expressions are $\boxed{\text{(C) equal whenever }  a + b + c = 1.}$