I recently wrote an article for Edutopia about factoring polynomials using areas and why FOIL is absolute crap:
For one, I’m not a fan of FOIL (first-outside-inside-last) for a plethora of reasons. While I think it’s handy to have an acronym that reminds students of a procedure, it only works in a very special case. In this case, FOIL works only for multiplying a binomial by another binomial. Does FOIL lead students toward understanding multiplication of all types of polynomials, or understanding why the distributive property works even with variables? I’m not so sure.
Please do let me know what you think about it! And please do encourage me to write more about math. I could use it in the coming school year!