Proving that $(A \cup B)^* = A^*(BA^*)^*$

2018-03-22 00:02:24

I would like to prove that $(A \cup B)^* = A^*(BA^*)^*$, where * means the Kleene star.

I would like to use induction to prove this equality but I do not how to proceed and how is the best way to set the induction hypothesis.

Could someone please help? Thanks !