I LOVE when I can bring the life of a mathematician into a lesson. Binomial Theorem/Expansion is a great example of this!
I always introduce Binomial Expansion by first having my student complete an already started copy of Pascal's Triangle. This is one warm-up that every student does without prompting. They see it as a puzzle and not "math" but you may have to encourage students to keep looking for the pattern. When they enter the classroom, I hand them the sheet, wear a beret, and only speak in French. My french is limited and it is easy to see who the French students are on how they respond to my questions. I keep up the French speaking through the warm-up and then I go into the life of Blaise Pascal. (Source: http://en.wikipedia.org/wiki/Blaise_Pascal)
Once that is done I introduce Binomial Expansion and tie that into Pascal's Triangle. I find that this method makes Binomial Expansion a little more exciting. Now, while I find BE very thrilling and life-changing, my students typically do not. I find the French speaking and little history lesson make a somewhat less thrilling topic a little more exciting.
I also recommend teaching your students how to logically expand these problems and not have them memorize the different formulas. This is a concept were students can pick up on the pattern quickly and ignore the formal definition of the formula!
Educator who loves math and working with students.