Affine spaces/Product/Basis/Exercise

Let $E$ and $F$ be affine spaces over the field $K$, and let an affine basis $P_1,\dots ,P_n$ of $E$ and an affine basis $Q_1,\dots ,Q_m$ of $F$ be given. Show that

$(P_1,Q_1),(P_1,Q_2),\dots ,(P_1,Q_m),(P_2,Q_1),(P_3,Q_1),\dots ,(P_n,Q_1)$

is an affine basis of the product space $E\times F$.

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