the way of writing eqn is wrong...

**the eqn R = Q+RP, ===> R = QP* when P is free from ϵ**

Q_{1} = *ϵ* + Q_{1} b + Q_{2} b ====> Q_{1} = (* ϵ* + Q_{2} b ) b*

Q_{2 }= Q_{1}.a + Q_{2}.a = (* ϵ* + Q_{2} b ) b* a + Q_{2} . a = b* a + Q_{2} . b . b* . a + Q_{2} . a

= b* a + Q_{2} . ( b . b* . a + a ) = b* a + Q_{2} . ( b^{+} a + a ) = b* a + Q_{2} . ( b^{+} + *ϵ* ) a = b* a + Q_{2} . ( b* ) a .

∴ Q_{2 }= b* a + Q_{2} . ( b* a ) ====> Q_{2} = b* a ( b* a )*

only Q_{2} is the final state, RE = b* a ( b* a )*