5-10 Let $A$ and $B$ be the sums of the odd and even terms, respectively, in the expansion of $(x+a)^{n}$. Find $A^{2}-B^{2}$.


[Solution] Clearly, $A+B=(x+a)^{n}$,
$$
A-B=(x-a)^{n} \text {, }
$$

Therefore,
$$
\begin{aligned}
A^{2}-B^{2} & =(x+a)^{n}(x-a)^{n} \\
& =\left(x^{2}-a^{2}\right)^{n} .
\end{aligned}
$$