Let me explain this rule by taking examples
96^2 :-
First calculate 100-96, it is 4
so 96^2 = (96-4)----4^2 = 9216
similarly
106^2 :-
First calculate 106-100, it is 6
so 106^2 = (106+6)----6^2 = 11236
Example.
An other case arises
110^2 = (110+10)----100 = (120+1)----00 = 12100
similarly
89^2 = (89-11)----121 = (78+1)----21 = 7921