How to show all possible implied parenthesis?
I'm assuming the input expression does not contain parentheses.

The idea is that for each binary operator we pick it as the principle operator (which is at the root of the parse tree) and split the expression into two subexpressions.
Then we solve the subproblems recursively.
After that we combine those solutions prepending and appending parens and inserting the principle operator in the middle. Notice that there could be multiple solutions for both subproblems.

Also you need to figure out the base case for recursion.