Squaring n-bit int vs. multiplying two n-bit ints

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 multip

Answer 1

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 :)