You simply need baking soda, a sponge and water.

Pour some baking soda into a bowl, add some water and pour it on the floor. Scrub with the sponge, using a little force between the joints, then mop as you usually do.

It is not necessary to use a cleaning product. On the contrary, using a little vinegar as an alternative to floor detergent will help disinfect surfaces and make your home smell nice.

You will see that with this simple trick the floor joints will be as good as new.