Cleaning floor tile grout makes most people grimace. I clearly remember scrubbing and scrubbing and seeing little improvement. That's why years ago I threw in the towel and just let the grout get dirtier. When I used oxygen bleach for the first time, I couldn't believe it. After soaking on the grout by itself, much of the grime and stains came up with little effort. A second soaking and a little scrubbing in the worst areas made the grout look like the day I installed it.
Some tile floors are installed adjacent to carpeting. If the oxygen-bleach solution gets onto the carpet, it will actually clean that, too. In fact, to clean carpeting with oxygen bleach, you simply mix up the solution and use a sprayer to saturate the carpet fibers. Let the solution soak for 30 minutes, and then use a regular carpet shampoo machine to finish the job.