Here is why I believe that the FOIL method for multiplying two binomial expressions should NOT be used:
The underlying premise of the FOIL method is that students must first be able to identify a binomial. However, most instructors do not seem to stress enough that the FOIL method can only be used to multiply two binomials. We can only speculate on the reason for why they might not do this – Maybe they only teach multiplying binomials so they do not need to make any distinction or maybe whey wrongly assume that students will be able to identify a binomial. However, in my opinion, if a student cannot identify a binomial, then they should not even be using the FOIL method.
Either way, what worries me the most is that fact that a student will get to a problem that involves multiplying expressions that are not binomials and will not know what to do. If I would have taught the student the distributive property that can be used in every case, rather than the FOIL method that can only be used in the special case of multiplying two binomials, wouldn’t that have been a better use of class time?
I have also had students who have asked me if they can use the FOIL method to multiply two trinomials and I, of course, tell them that they cannot. But then the student objects because they have just multiplied two trinomials using the FOIL method and want to show me that their answer is correct.
Even in the cases when the student has shown correct work and has arrived at the correct answer, I still have to cringe at the fact that the FOIL method involves the student multiplying four times and multiplying two trinomials involves the student multiplying nine times, but the student still wants to argue about the fact that he can use the FOIL method on every problem. There is a big difference between four multiplications and nine multiplications.
I honestly believe that students would benefit more if we simply dropped the FOIL method and instead taught them the distributive property along with a review of counting properties by asking them to count how many different multiplications must be done before they even begin. It is definitely one way that we could help increase ‘number sense’ in our students.
And ultimately, FOIL is for baked chicken, NOT for multiplying binomials.