The function f(x) has the property that f (x+y) = f(x)+f(y)+2xy, for all positive integers x and y. If f(1) = 4, then what is the value of f(8)?
So, this is a really fun pattern problem. Now, since you already know f(1), it will be advantageous to write f(1+y) as f(n), and say that for f(8), y=7. Then start checking to see if there's a pattern which you can gneralize in terms of n, while n=y+1. Remember that f(x) is a known variable, and that y equals n-1. A hint: remember the factorials.