When bleach and baking soda are mixed, the cleaning properties of both are improved. For instance, when both baking soda and chlorine bleach are used on dirty laundry, the clothes come out cleaner and fresher. This happens when only 1/2 cup of baking soda is added to a typical laundry load with bleach.
However, bleach should definitely not be mixed with certain other common household products because toxic gases form. Ammonia or substances made with ammonia, such as window cleaner, must never be combined with bleach. Gases are released that cause difficulty breathing and throat, nose and eye irritation. Also, vinegar and bleach are a dangerous pairing. Chlorine gas develops, and high levels of it are deadly.