Question: Disclaimer: Homework question. I'm looking for a hint…

Professor F. Lake tells his class that it is asymptotically faster to square an n-bit integer than to multiply two n-bit integers. Should they believe him?

I believe that multiplying two n-bit ints via shift/add is an O(n) operation, but I can't see why squaring an n-bit int would be any different. Am I missing something?

Answer: 
Since you wanted only a hint, answer comes from this equation: `(a + b)^2 = a^2 + b^2 + 2*a*b` 

To not spoil the puzzle, I've posted complete solution [separately](http://jsfiddle.net/DqpLm/1/) :)
Consider the steps the computer needs to take in order to accomplish these tasks. Remember that computers work drastically different from people.