Suppose that a function $f$ defined on $\mathbb{R} ^2$ satisfies the following conditions:
$$\begin{array} &f(x+t,y) & = & f(x,y)+ty, \\ f(x,t+y) & = & f(x,y)+ tx \text{ and } \\ f(0,0) & = & K, \text{ a constant.} \end{array}$$
Then for all $x,y \in \mathbb{R}, \:f(x,y)$ is equal to