Answer
$\text{not a monomial}$
Work Step by Step
Monomials have the form:
$$ax^k$$
where $a$ is a constant, $x$ is a variable, and $k$ is a non-negative integer (the degree).
Monomials in two variables have the form:
$$ax^ny^m$$
where $x$ and $y$ are both considered the "variables" with the degree being the sum $n+m$.
The expression $x^2+y^2$ is not a monomial because it does not match either form above (as it is a sum of two terms).