I assembled these with polyurethane (Gorilla) glue and 1" staples. I have made a number of drawers this way over the past few years, and none of them have come apart.
These large drawers are really wide at 36". They are sized to hold blankets and pillows.
Today I will mount the drawer slides and hopefully get the fronts made. I always use the heavy-duty, full extension slides and stay away from the cheap "euro" ones. I use to use the cheaper ones, but had a number of problems with them, and I think they make a project feel like it's lower quality.