13.7 If real numbers $a, b, c$ satisfy $a^{2}+b^{2}+c^{2}=9$, then the maximum value of the algebraic expression $(a-b)^{2}+$ $(b-c)^{2}+(c-a)^{2}$ is
(A) 27.
(B) 18.
(C) 15.
(D) 12.
(China Junior High School Mathematics League, 1997)
[Solution] Notice the algebraic expression:
$$
\begin{aligned}
& (a-b)^{2}+(b-c)^{2}+(c-a)^{2} \\
= & a^{2}-2 a b+b^{2}+b^{2}-2 b c+c^{2}+c^{2}-2 c a+a^{2} \\
= & 3\left(a^{2}+b^{2}+c^{2}\right)-\left(a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a\right) \\
= & 27-(a+b+c)^{2} \leqslant 27 .
\end{aligned}
$$

Therefore, the answer is $(A)$.