We consider a natural integer $n$ and a complex number $a$. We define a family of polynomials $(A_0, A_1, \ldots, A_n)$ by setting
$$A_0 = 1 \quad \text{and, for all } k \in \llbracket 1, n \rrbracket, \quad A_k = \frac{1}{k!} X(X - ka)^{k-1}.$$
Using the result of Question 24, deduce Abel's binomial identity:
$$\forall (a, x, y) \in \mathbb{C}^3, \quad (x+y)^n = y^n + \sum_{k=1}^{n} \binom{n}{k} x(x - ka)^{k-1}(y + ka)^{n-k}.$$