 Whitney sum formula for Chern classes

The Total Chern class of a direct sum of complex vector bundles is the product of their total Chern classes. In each degree, $c_k(E\oplus F)={\sum }_{i+j=k}{c}_i(E)⌣c_j(F)$. The degree-zero class is one, classes beyond the bundle rank vanish, and a trivial bundle has total class one.