Several formulas for multiplication of polynomials by polynomials (a+b)(c+d)= (a+b)(c-d)= (a-b)(c+d)= (a-b)(c-d)= How to write these formulas?

1 ac+bc+ad+bd
2 ac+bc-ad-bd
3 ac+ad-bc-bd
4 ac-bc-ad+bd
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1. 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?
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