a² = (a-1)*(a+1) + 1

a^2 = (a-1)*(a+1) + 1

example:
999^2 = (998)*(1000) + 1
998001 = 998000 + 1

isn't it great?
well, you can change the 1 by whatever:
a^2 = (a-n)*(a+n) + n^2

so like, 3^2 = 2*4 - 1
I dig