1.12 Algebraic expressions $a+b c$ and $(a+b)(a+c)$
(A) are equal.
(B) are never equal.
(C) are equal when $a+b+c=1$.
(D) are equal when $a+b+c=0$.
(E) are equal only when $a=b=c=0$.
(6th American High School Mathematics Examination, 1955)
［Solution］ If we set $a+b c=(a+b)(a+c)$,
then
$$
a+b c=a^{2}+(b+c) a+b c,
$$

which means $\square$
$$
a=a^{2}+(b+c) a .
$$

If $a \neq 0$, then $a+b+c=1$;
If $a=0$, then $\circledast$ still holds.
Therefore, the answer is $(C)$.