14.4 Scalar Triple Product

Prove that for any three non-zero vectors $\mathbf{u}$, $\mathbf{v}$ and $\mathbf{w}$, $(\mathbf{u} + \mathbf{v}) \cdot [(\mathbf{v} + \mathbf{w}) \times (\mathbf{w} + \mathbf{u})] = 2[\mathbf{u}\,\mathbf{v}\,\mathbf{w}]$.