  We find bivariate generating functions for the $k=1$ cases of recently
conjectured colored partition identities of Capparelli, Meurman, A. Primc, and
M. Primc that are slight variants of the generating functions for the sum sides
of the Andrews-Gordon and Andrews-Bressoud identities. As a consequence, we
prove sum-to-product identities for these cases, thus proving the conjectures.
