Question

How do you determine if `f(x,y)=-x^3+3x^2y^2-2y^2` is homogeneous and what would it's degree be?

Answer 1

You want to check that `P(lambda x, lambda y) =lambda^n P(x,y)` That can not be the case since P is the sum of three terms of unequal degree. So the answer is no.