I need to find a and b with whom this expression is associative: $x\bullet y=(a+x)(b+y)$ Also known that $x,y\in Z$ So firstly I write: $(x\bullet y)\bullet z=x\bullet (y\bullet z)$ Then I express and express them and after small algebra I get: $ab^2+b^2x+az+abz+bxz=a^2b+a^2z+bx+abx+axz$ And I don't know what to do now, I don't know if I should do it, but I tried to assign to $x=0$ and $z=1$ but nothing better happened.
Could you please share some ideas?
EDIT: Sorry, but I forgot to mention that I need to find such a and b with whom it should be associative