regular expression

Question

write regular expression for  atmost   2 a's  over ∑ = {a , b }   , i know its easy but plz reply  , then i can tell what i have problem in this

Comments

b* + b*ab* + b*ab*ab*

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is this correct  :   L  =  { ε ,a , b , aa ,ab , ba ,bb }

is this is correct language for this according to u bro  

final regular expression :  ( a+ b +ε) ( a+b+ε)  

my question is : input alphabet is  {a,b} . it cannot contain null  , why we took  ε in language, for  ε to be included in language it should be {a,b}* 

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@Sumit becuase language is the subset of $Σ^{*}$ where Σ={a,b}

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got it thnks