You're right to think there are strategies for dealing with a product, but you should also have a quick look to see if it doesn't split into a sum of easy ones... i.e. multiply out
(x-1)(x+1) this is an integral question.
I know how to integrate but I am not sure what to do when you have two pairs of brackets. I know how to do a question like (2x+1)^2. Can some one please help me get a start.