Tensor product/Direct sum/Fact

Let ${}K$ be a field, and let ${}U,V,W$ denote ${}K$ -vector spaces.

Then we have

{}U\otimes _{K}{\left(V\oplus W\right)}\cong {\left(U\otimes _{K}V\right)}\oplus {\left(U\otimes _{K}W\right)}\,.