Mixed volume is Multi-linear

Prove that mixed volume is multilinear respect to Minkowski sum: For polytopes $P,Q,P_2,\dots,P_n \subset \mathbb{R}^n$ and non-negative real numbers $\lambda$ and $\mu$,

(1)
\begin{align} \operatorname{MV}(\lambda\, P+ \mu\, Q, P_2,\dots,P_n) = \lambda \cdot \operatorname{MV}(P,P_2,\dots,P_n) + \mu \cdot \operatorname{MV}(Q,P_2,\dots,P_n). \end{align}
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