Simplify this regular expression

[compsciguyyy]

I'm unsure if this regular expression can be simplified, if it can, could you please explain how?

Thank you!

(a U b)*(a U e)b* U (a U b)*(b U e)a*

The e is the empty string, and the U stands for union.

 

[Bill Simpson]

Start with baby steps.

Describe all the strings in (a U b)*.
Then describe all the strings in (a U b)*(a U e).
Are the two sets different? Are the two sets the same? Why or why not?
Can you learn something from this that you can apply to another part of the problem?
Can you learn something from all this to answer the question?