Barycentric coordinates/Point difference/Exercise

Let ${}E$ be an affine space over the ${}K$-vector space ${}V$. Let ${}P_{i}$, ${}i\in I$, and ${}P,Q$ denote points in ${}E$, and let ${}\sum _{i\in I}a_{i}P_{i}$ be a barycentric combination. Show that

${}P-Q+\sum _{i\in I}a_{i}P_{i}={\overrightarrow {QP}}+{\left(\sum _{i\in I}a_{i}P_{i}\right)}\,$

holds, where the left-hand expression is a barycentric combination.

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