1.42 If $a-b=2, a-c=\sqrt[3]{7}$, then the value of the algebraic expression
$$
(c-b)\left[(a-b)^{2}+(a-b)(a-c)+(a-c)^{2}\right]
$$

is
(A) 1 .
(B) -5 .
(C) 9 .
(D) 15 .
(E) None of the above answers is correct.
(Beijing Junior High School Mathematics Competition, 1983)
[Solution] From the given, we have
$$
\begin{aligned}
& (c-b)\left[(a-b)^{2}+(a-b)(a-c)+(a-c)^{2}\right] \\
= & {[(a-b)-(a-c)]\left[(a-b)^{2}+(a-b)(a-c)+(a-c)^{2}\right] } \\
= & (a-b)^{3}-(a-c)^{3}=2^{3}-(\sqrt[3]{7})^{3}=1 .
\end{aligned}
$$

Therefore, the answer is $(A)$.