A1. For numbers $x$ and $y$, the relation $(x+2 y)^{2}-3 y(y-1)=(2 x+y)^{2}-3 x(x+1)$ holds. What is their sum $x+y$?
(A) -100
(B) -1
(C) 0
(D) 1
(E) cannot be uniquely determined
A1. After squaring and removing the parentheses, we get $x^{2}+4 x y+4 y^{2}-3 y^{2}+3 y=4 x^{2}+4 x y+y^{2}-$ $3 x^{2}-3 x$. The equation simplifies to $3 y=-3 x$, or $x+y=0$. The correct answer is C.