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

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