  Recently, Bjerrum-Bohr, Damgaard, Feng and Sondergaard derived a set of new
interesting quadratic identities of the Yang-Mills tree scattering amplitudes.
Here we comment that these quadratic identities of YM amplitudes actually
follow directly from the KLT relation for graviton-dilaton-axion scattering
amplitudes (in 4 dimensional spacetime). This clarifies their physical origin
and also provides a simpler version of the new identities. We also comment that
the recently discovered Bern-Carrasco-Johansson identities of YM helicity
amplitudes can be verified by using (repeatedly) the Schouten identity. We also
point out additional quadratic identities that can be written down from the KLT
relations.
