# simple question about covariance

Let $x,y,z$ be three random variables. How can you show that: $$\operatorname{cov}(x+y,z) = \operatorname{cov}(x,z) + \operatorname{cov}(y,z)$$ by using the definition of covariance.

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Use the fact that $cov(X,Y)=E(X-EX)(Y-EY)$ and rearrange the terms. I've included the full solution below, just move the mouse on the grey area.