We present a study of the impact of the expansion of deconfined medium on single-gluon emission spectra and the jet suppression factor ($Q_{AA}$) within the BDMPS-Z formalism. These quantities are calculated for three types of media (static medium, exponentially decaying medium and Bjorken expanding medium). The distribution of medium-induced gluons and the jet $Q_{AA}$ are calculated using the evaluation of in-medium evolution with splitting kernels derived from the gluon emission spectra. Scaling behavior of splitting kernels is derived for low-x and high-x regimes in the asymptote of large times and its impact on the resulting jet $Q_{AA}$ is discussed. For the full phase space of the radiation, the scaling of jet $Q_{AA}$ with an effective quenching parameter is presented.