One technique I like to use when doing any kind of multiplication is to round the numbers, multiply, then add the multiplication of the remainders together. 222 * 15 = 200 * 15 + (15 * 22) = 3000 + (15 * 20) + (15 * 2) = 3000 + 30 + 300 = 3330.

I would do this for all multiplication basically, though. I really like the trick presented here for doing squares. It will make life much easier if I can just remember the formula.