Let $Q$ be a delta endomorphism with associated polynomial sequence $(q_n)_{n \in \mathbb{N}}$. Show that, for every natural number $n$, $$\forall (x,y) \in \mathbb{K}^2, \quad q_n(x+y) = \sum_{k=0}^n q_k(x) q_{n-k}(y)$$
Let $Q$ be a delta endomorphism with associated polynomial sequence $(q_n)_{n \in \mathbb{N}}$.
Show that, for every natural number $n$,
$$\forall (x,y) \in \mathbb{K}^2, \quad q_n(x+y) = \sum_{k=0}^n q_k(x) q_{n-k}(y)$$