Let $k$ be an algebraically closed field. Let $C, D$ be curves in $\mathbb{P}^2_k$ defined by homogeneous polynomials $F, G$ of degrees $c, d$ respectively. Suppose $C$ and $D$ share no irreducible component. Then $|C \cap D| \leq cd$. Moreover, there exist integers $m_p \geq 1$ for each $p \in C \cap D$ such that
\begin{align*}
\sum_{p \in C \cap D} m_p = cd.
\end{align*}