In Hatcher's book pp.54 there is an isomorphism between product of K-theory and that of reduced K-theory
$$K(X) \otimes K(Y) \cong \left(\widetilde{K}(X) \otimes \widetilde{K}(Y)\right) \oplus \widetilde{K}(X) \oplus \widetilde{K}(Y) \oplus \mathbb{Z}$$
Could somebody explain what this isomorphism is?