Responses/hints to Puzzle #12

 

                  To expand on the hint, you need to know/learn that:

 

                  (a-b)2 = a2 - 2ab + b2 and (a+b)2 = a2 + 2ab + b2

 

                  Now complete the following addition problem:

 

                                     (a-b)2  =  a2 - 2ab + b2

                                     +4ab  =      +4ab    

                                    ????   =  a2 + ??? + b2