Consider the subring R of Q[x,y] consisting of all $h(x,y)=a_0 + a_1x + a_2y + a_3xy + a_4x^2 + a_5y^2 + a_6x^2y + a_7xy^2 +’a_8x^3 + ...$ where all $a_i$ are in Q and a_1 = a_2 = 0.
I’m suppose to prove R is a unital subring if Q[x,y] and that x.y is irreducible in R, but not prime.
I know when x & y are 0 or 1 , then R subset of Q, but I think I’m going about this the wrong way