For even no a's RE (b*ab*ab*)* + b* correct or (b*ab*ab*)*.b* or both are equal

Question

For even no a's  RE  over  {a,b}  

1) (b*ab*ab*)* + b*  

2) (b*ab*ab*)*.b*  

3) both are equal?

which one is correct?

Comments

both are same and can be used for generating even no of a's.

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Yes Both are same, accepts the even number of a's but the second RE also tries to accept of any number of b's due to concatenation.
Sry fr the wrong ans

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Both are same. multiple expression are possible for any given language.

Answer 1

$(b^*ab^*ab^*)^*+b^* \equiv (b^*ab^*ab^*)^*b^* \equiv b^*(b^*ab^*ab^*)^* \equiv b^*(ab^*ab^*)^* \equiv (b^*ab^*a)^*b^*$