$(a \lor b) a a^*(a \lor a a^*b) \lor (a \lor b)aa^*aa^*$ is wrong?

Question

Here is the non-deterministic finite automaton. I want to find the reguluar expression related to this diagram. I found $(a \lor b) a a^*(a \lor a a^*b) \lor (a \lor b)aa^*aa^*$, but it seems my answer is wrong. Where am I making an error?

Answer 1

$(a \cup b) (a \ (a \cup b)) ^* aa^*\{b \ (a \cup b) (a \ (a \cup b)) ^* aa^*\}^*$