Question 88430
For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x^2y^2 + 3x^3 + 4y has degree 4, the same degree as the term x^2y^2.

However, a polynomial in variables x and y, is a polynomial in x with coefficients which are polynomials in y, and also a polynomial in y with coefficients which are polynomials in x.

x^2y^2 + 3x^3 + 4y = (3)x^3 + (y^2)x^2 + (4y) = (x^2)y^2 + (4)y + (3x^3) 
This polynomial has degree 3 in x and degree 2 in y.
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Your Problem:
8x^3 + 6x^2y + 4xy^3 - 2y^4  has degree 4 
As a polynomial in y it has degree 4
As a polynomial in x it has degree 3
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Cheers,
Stan H.