1.4 Simplify $\frac{a^{4}-a^{2} b^{2}}{(a-b)^{2}} \div \frac{a(a+b)}{b^{2}} \cdot \frac{b^{2}}{a}$, the result is
(A) $\frac{a^{2}}{a-b}$.
(B) $\frac{a^{2}}{a+b}$.
(C) $\frac{b^{4}}{a-b}$.
(D) $\frac{b^{4}}{a+b}$.
(China Beijing Junior High School Mathematics Competition, 1982)
[Solution] Notice that
$$
\begin{aligned}
& \frac{a^{4}-a^{2} b^{2}}{(a-b)^{2}} \div \frac{a(a+b)}{b^{2}} \cdot \frac{b^{2}}{a} \\
= & \frac{a^{2}(a+b)(a-b)}{(a-b)^{2}} \cdot \frac{b^{2}}{a(a+b)} \cdot \frac{b^{2}}{a} \\
= & \frac{b^{4}}{a-b} .
\end{aligned}
$$

Therefore, the answer is $(C)$.