$f(x, y)$ is homogeneous of degree 2 and $g(x, y)$ is homogeneous of degree 3. What is the degree of the homogeneous function $f(x, y)\,g(x, y)$?

Explanation

1. 01

   $f(\lambda x, \lambda y)\,g(\lambda x, \lambda y) = \lambda^{2}f \cdot \lambda^{3}g = \lambda^{5}fg$.

2. 02

   The powers of $\lambda$ add, so the degree is 5.