[en] Adopting OFDMA and MU-MIMO techniques for both downlink and uplink IEEE 802.11ax will help next-generation WLANs efficiently cope with large numbers of devices but will also raise some research challenges. One of these is how to optimize the channelization, resource allocation, beamforming design, and MCS selection jointly for IEEE 802.11ax-based WLANs. In this paper, this technical requirement is formulated as a mixed-integer non-linear programming problem maximizing the total system throughput for the WLANs consisting of unicast users with multicast groups. A novel two-stage solution approach is proposed to solve this challenging problem. The first stage aims to determine the precoding vectors under unit-power constraints. These temporary precoders help re-form the main problem into a joint power and radio resource allocation one. Then, two low-complexity algorithms are proposed to cope with the new problem in stage two. The first is developed based on the well-known compressed sensing method while the second seeks to optimize each of the optimizing variables alternatively until reaching converged outcomes. The outcomes corresponding to the two stages are then integrated to achieve the complete solution. Numerical results are provided to confirm the superior performance of the proposed algorithms over benchmarks.