To better understand the physics underlying the eruption of prominences in solar active regions, we studied eruption processes of two active prominences located in the active region NOAA 11261 using multi-wavelength observational data with high temporal and spatial resolution. Specifically, we examined (1) the temporal variation of morphology and plasma properties of the two active prominences, (2) magnetic fields and their evolution on the photospheric surface underneath the prominences, and (3) the time profiles and locations of radio, EUV, and soft/hard X-ray emissions produced by the M9.3 flare related to the prominence eruption. As a result, we found that: (1) a prominence F1 began to erupt and expand as the abrupt and intense EUV brightening occurred in the localized region underneath the western part of F1 at 03:45 UT prior to the peak time of the M9.3 flare, (2) F1 split into two parts: i.e., the western part asymmetrically erupted by producing the M9.3 flare with microwave source motions along the magnetic polarity inversion line between the two flare ribbons, while the eastern part coalesced into a pre-existing prominence F2, (3) F2 became unstable due to the coalescence with the eastern part of F1, and then it partially erupted with clockwise untwisting motions.