  We demonstrate that the tree level amplitudes and the explicit formulas of
soft factors can be uniquely determined by soft theorems and the universality
of soft factors. By imposing the soft theorems and the universality, as well as
the assumption of double copy, we reconstruct single trace Yang-Millsscalar
amplitudes and pure Yang-Mills amplitudes, in the expanded formulas. The
explicit formulas of soft factors for the bi-adjoint scalar and gluon are also
determined. The expansions of Yang-Mills-scalar and Yang-Mills amplitudes can
be extended to Einstein-Yang-Mills and gravitational amplitudes, and we use the
expanded single trace Einstein-Yang-Mills amplitudes to reproduce the soft
factors for the graviton.
