# How to reduce this regular expression?

I was converting a DFA to regular expression with the help of state equations and came up with this regular expression. How do I further reduce this regular expression? $$b+aaa^*b+abb^*+a$$ I can feel it's same as $$a^*b+ab^*$$ but how do I proceed to simplify the first one to the second mathematically?

$$abb^* + a = ab^*,$$
since $ab^* = a(b^*) = a(\varepsilon + b b^*) = a + abb^*$.