The Box Method of multiplying polynomials has been very much preferred by my Algebra 2 students, even over the FOIL method. it is because it places each of the partial products in an organized location on a grid.
I use the following set of notes, vocabulary and practice problems with illustrations to describe multiplying two polynomials using the box method. As the complexity of the problems increase, my students become more proficient. The process even reinforces the concept of matrix dimensions, taught earlier in the class.
The notes include 4 cases of polynomial multiplication:
- a monomial times a binomial
- a binomial times a binomial
- a binomial time a trinomial
- a trinomial times a trinomial
I cover the notes as the students fill in the vocabulary sheet, some of the definition I provide on the overhead, other I ask the students to write in their own words. Then we attack the practice problems.