Because most math teachers start with FOIL, I

*started there. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product. Inner is for "inside" so those two terms are multiplied—second term of the first binomial and first term of the second). Last is multiplying the last terms of each binomial.*My student could keep FOIL in his head, but couldn't quite remember what the letters represented, let alone which numbers to multiply; so, that method was quickly laid aside.

I next tried the Box Method. Immediately, it made sense to him, and we were off to the races, so to speak. He continually got the right answer, and his confidence level continued to increase. Here is how the Box Method works.

First, you draw a 2 x 2 box. Second, write the binomials, one along the top of the box, and one binomial down the left hand side of the box. Let's assume the binomials are 2

*x*+ 4 and*x*+ 3.**(2**

*x*+ 4) (*x*+ 3)Now multiply the top row by

*x*; that is*x*times 2*x*and*x*times +4., writing the answers in the top row of the box, each in its own square. After that, multiply everything in the top row by +3, and write those answers in the second row of the box, each in its own square.Looking at the box, circle the coefficients that have an

*x*. They are located on the diagonal of the box.To find the answer, write the term in the first square on the top row, add the terms on the diagonal, and write the number in the last square on the bottom row. Voila! You have your answer!

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