May I ask the general expression and number of terms of bivariate polynomials of higher degree The bivariate polynomial is Z = A0 + A1 * x + A2 * y, and there are three terms; The bivariate quadratic polynomial is Z = A0 + A1 * x + A2 * y + a3 * x * x + A4 * x * y + A5 * y * y, with 6 terms; So if it is a binary m-degree polynomial, how to express it? What is the total number of terms?

May I ask the general expression and number of terms of bivariate polynomials of higher degree The bivariate polynomial is Z = A0 + A1 * x + A2 * y, and there are three terms; The bivariate quadratic polynomial is Z = A0 + A1 * x + A2 * y + a3 * x * x + A4 * x * y + A5 * y * y, with 6 terms; So if it is a binary m-degree polynomial, how to express it? What is the total number of terms?

z=∑a[i,j,i+j≤m]x^iy^j
A [I, J, I + J ≤ M] is the coefficient, I and j are the subscripts of a non negative integer
There are 1 + 2 +... + m + m + 1 = (M + 1) (M + 2) / 2 terms