Lp norm

hi
i need to find an inequality between
|f-g|^2
and
|f|^2 - |g|^2

i need to show that the first one is bigger and why

|f| stands for abs

the original question is about hamiltionian of NLS under H1 norm

thanks

the original question said to show that if the first one goes to 0
then the other one also goes to 0