Why is squaring a number faster than multiplying two random numbers?

Question

Multiplying two binary numbers takes n^2 time, yet squaring a number can be done more efficiently somehow. (with n being the number of bits) How could that be?

Or is i

Answer 1

a^2 (a+b)*(a+b)+b^2 eg. 66^2 = (66+6)(66-6)+6^2 = 72*60+36= 4356

for a^n just use the power rule

66^4 = 4356^2