Take any string of the form wxwr.
Let w be anything other than epsilon as w ∈ (0,1)+ . I take 01011 then wr becomes 11010.
wxwr = 01011 x 11010
I can extend this x in both directions to consume all the symbols leaving only the symbols at the 2 extremes.
01011 x 11010
I can say my new xnew is 1011xold1101. (xold,xnew∈ (0,1)+ )
wnew,wnewr becomes 0 and 0.
So I can write like wnewxnewwnewr. (wnew,wnewr∈ (0,1)+).
Now see that this is also in form of wxwr. It is not mandatory to choose a particular w and then proceed. Just check whether a string can be represented in this given form or not maintaining the constraints.
Similarly take any other string and same thing can be done for them.