# regular languages – How to choose word for pumping lemma for \$a^kb^{2k}a^k\$?

I have to show that the language $$mathcal {L} = {a ^ k b ^ {2k} a ^ k: k geq 0 }$$ is not a regular language. So that’s what I want to use the pumping motto for. What I could do is this: let $$sigma = a^Nb^{2N}a^N$$, where $$| sigma | = 4N geq N$$, fulfilling that $$alpha beta^k gamma$$. But at the moment of being able to separate $$alpha beta$$ I am very complicated and I cannot reach the possible cases.