Question 6
The function $f(x,y)$ is a homogeneous polynomial of the $n$th degree in $x$ and $y$. If $f(1,0)=1$ and for all $a,b,c$,
$$f(a+b,c)+f(b+c,a)+f(c+a,b)=0,$$
prove that $f(x,y)=(x-2y)(x+y)^{n-1}$.
$$f(a+b,c)+f(b+c,a)+f(c+a,b)=0,$$
prove that $f(x,y)=(x-2y)(x+y)^{n-1}$.