Distribution of Matrix and Vector products

Given the following expression:

$$\vec w = (\mathbf M\cdot\vec u) + (\vec v\cdot\vec u)$$

Where $\mathbf M$ is a matrix of dimension $n\times m$, $\vec v$ and $\vec u$ are vectors of dimension $m$, and $\vec w$ is a vector of dimension $n$. Is there a way to apply the distributive property such that we can say

$$\vec w = \mathbf X\cdot\vec u$$

Where $\mathbf X$ is a matrix (or maybe something else)?

Thanks.

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