Daniel,
I'm not sure what the question marks represent in your problem statement ?(x+y)?^2 = x^2 + y^2 , so I will ignore them in my solution. If this is incorrect, please restate the problem for me. Thanks.
So the relation would be (x + y)^{2} = x^{2} + y^{2} if the question marks are removed. If we are talking about integers: .. 2, 1, 0, 1, 2, ... then
by crossmultiplying we get x^{2} + 2xy + y^{2} = x^{2} + y^{2}, which would mean 2xy = 0, so x = 0 or y = 0. So the statement is true if either x or y is equal to zero, and otherwise it's false.
But let's explore this a bit further.
Suppose you were working on a number system that was like the integers but not exactly  say on a 6hour clock. So that, for example, 2*3 = 6
which is equal to 0 on a 6hour clock. So on this 6hour clock, if x = 2 and y = 3, then xy = 0 and we would have (x + y)^{2} = x^{2} + y^{2 }where neither x nor y was zero. So it really depends which number system you are
working on whether an equality like this holds.
1/27/2014

Kenneth G.