The expository essay is a genre of essay that requires the student to investigate an idea, evaluate evidence, expound on the idea, and set forth an argument concerning that idea in a clear and concise manner. And the method used when writing this type of essay is comparison and contrast.
Well an expository essay is a writing peice that explains your topic or whatever you plan to write about and when you write you can really use any method but it has to sound right and feel right.