Question about a functional equation

[green forum]

,, f(x+yf(x))+f(xf(y)-y)=f(x)-f(y)+2xy^2 \text{ }\forall (x,y)\in\mathbb{R}\times\mathbb{R}

[burnt pine]

isanath

[pastel hill]

is it just $2xy^2$ or $2(xy)^2$

[burnt pine]

autocrazizt

[green forum]

I see, the equation is symmetrical with respect to $x$ and $y$, which leads to $2xy^2=2yx^2$ for all $x$ and $y$ which is abusive, right?

[burnt pine]

isanath

[green forum]

Where does $2(xy)^2$ come from ?