Could any tell me if a multivariate polynomial generated from the sum of irreducible single variable polynomial is irreducible?
For example, f(x)=x^2+2x+2, g(x)=x^2+3x+3, h(x)=x^3+2x^2+2x+2 all of them are irreducible, then what about f(x,y,z) = f(x)+g(y)+h(z)?



Irreducibility for multivariate polynomial polynomial generated from sum of irreducible polynomial in one variable
$(x^2+1)-(y^2+1)=(x+y)(x-y)$


