For any commutative ring R, R[x, y] is the ring of polynomials in x and y with coefficie...

For any commutative ring R, R[x, y] is the ring of polynomials in x and y with coefficients in R (that is, R[x, y] consists of all finite sums of terms of the form ax_iy_j, where a ∈ R and i and j are nonnegative integers). (For example, x⁴ – 3x²y – y³ ∈ Z[x, y].) Prove that is a prime ideal in Z[x, y] but not a maximal ideal in Z[x, y].