28.30. Let $(x+a)^{n}=A_{0}+A_{1} x+\ldots+A_{n} x^{n}$. Find the coefficients $A_{0}, \ldots, A_{n}$ by successive differentiation.
28.30. For $x=0$ we get $A_{0}=a^{n}$. Differentiating the original equality, we obtain

$$
n(x+a)^{n-1}=A_{1}+2 A_{2} x+\ldots+n A_{n} x^{n-1}
$$

For $x=0$ we get $A_{1}=n a^{n-1}$. Differentiating the new equality, we obtain

$$
n(n-1)(x+a)^{n-2}=2 \cdot 1 \cdot A_{2}+3 \cdot 2 \cdot A_{3} x+\ldots+n(n-1) A_{n} x^{n-2}
$$

After $m$-fold differentiation ($m \leqslant n$), we obtain

$$
\begin{aligned}
& n(n-1) \ldots(n-m+1)(x+a)^{n-m}=m(m-1) \cdot \ldots \cdot 1 \cdot A_{m}+ \\
& \quad+(m+1) m \cdot \ldots \cdot 2 \cdot A_{m+1} x+\ldots+n(n-1) \ldots(n-m+1) A_{n} x^{n-m}
\end{aligned}
$$

Thus, $n(n-1) \ldots(n-m+1) a^{n-m}=m(m-1) \cdot \ldots \cdot 1 \cdot A_{m}$.