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$L$ = { $vwv$ : $v,w$ ∈ $(a+b)^* $ , $|v| = 2 $ }

$|v| = 2 $ leaves us with only 4 choices for $v$ : $ aa,ab,bb,ba $

So Regex for this language : $aa(a+b)^* aa$ $+$ $ ab(a+b)^* ab$ $+$ $ba(a+b)^* ba$ $+$ $bb(a+b)^* bb$

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