Problem 1 Find all functions f:R→Rf:\mathbb{R}\to\mathbb{R}f:R→R such that for all x,y∈Rx, y\in\mathbb{R}x,y∈R , we have f(x+y)+f(x)f(y)=f(xy)+(y+1)f(x)+(x+1)f(y).f(x+y)+f(x)f(y)=f(xy)+(y+1)f(x)+(x+1)f(y).f(x+y)+f(x)f(y)=f(xy)+(y+1)f(x)+(x+1)f(y).