 Polynomial growth of a finitely generated two-step nilpotent group

Every finitely generated two-step nilpotent group has polynomial growth of a group. If $s_1,\dots ,s_k$ generate it, centrality of the commutators collects every word of length at most $n$ intowhere $|a_i|\le n$ and $|b_{ij}|=O(n^2)$. There are therefore only polynomially many possible collected words.