I don't understand how to expand and simplify brackets such as (x-3)(x+5)

In my opinion, the best way to expand and simplify brackets is to use the FOIL method which stands for the following:F - firstsO - outersI - innersL - lasts.This means that you multiply the first numbers in both brackets together so in this case it would be x multiplied by x which would be x^2. Next you would look at the two numbers on the outside edges of the brackets (would show on diagram) which, in this case, would be x multiplied by 5 which equals 5x. This process needs to be continued until you have completed FOIL process, being careful of positive and negative signs. At the end you then need to collect like terms to make the answer look as 'neat' as possible. In this case the answer would be x^2+2x-15