Teeth whitening does not stop at the toothpaste level. Although it can be done at the dentist, it is very expensive. Cheaper alternatives are using teeth whitening products that you can get over the counter, such as Crest Whitening Strips or Plus White Whitening Gel. If not, baking soda can also be used as an even cheaper alternative where such products cannot be found.
Always ensure (check with your dentist, read the disclaimer notes) that your teeth and gums are able to handle these chemicals before you try them though. Just like with skin care products, there is no one thing that works equally for everybody.