One cool way of making a pure white background is to use your softbox as a background.
Use the biggest softbox that you have, but not so big that it will not produce an even exposure all over. It all depends on the flash-power inside. Turn the power down so it is about one stop brighter than your general reading. For this shot I used a reflected umbrella as the key-light and then positioned a silver/gold reflector on the opposite side to further soften up the shadows.
The softbox is so bright it actually spills some light over the subjects shoulders. But I kind of like that effect. If I had a bigger softbox I would probably move it further away to be able to stop it down a bit.
The model is my lovely 10-year-old daughter.