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  • $\begingroup$ Thank you for your help. Do you know any website where I can learn the equations you used to rewrite the expression? $\endgroup$ Commented Oct 22, 2020 at 16:03
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    $\begingroup$ No, sorry. What I used is just the definition of "plus". If $E$ is a regular expression then $E^+$ is defined as $EE^*$ (or equivalently $E^*E$). The equality $(ab)^+ = a(ba)^*b$ follows from the fact that both expression correspond to words with $k \in {2,4,6,\dots}$ alternations of "a" and "b". Therefore $(ab)^+ = ab(ab)^* = (ab)^*ab = a(ba)^*b$. $\endgroup$ Commented Oct 22, 2020 at 16:13