The method that you use in school, although correct, is not the method used by most (and when I say most-I mean almost all) institutions. A really good explaination of how these problems are done can be found here.
algebra.help -- Simplifying using the FOIL Method
BTW: Your method is not an "expansion" in the normal sense of the word, as someone has already mentioned. THe term expansion implies that there will be more terms after the mutiplication is complete (in most cases). And that thes terms may have likenesses.