Let X be an affine space in F^n and let Y be an affine space in F^k. We look now on the next Cartesian product:

X x Y = {(x,y)| x in X, y in Y} c F^n x F^k =~F^(n+k)

Prove that if to think on X x Y as subset of F^(n+k) under the identification:

((x_1,...,x_n),(y_1,...,y_k)) =(x_1,...,x_n,y_1,...,y_k)

so we get an affine space.