Origin of FOIL Method
While multiplying binomials several methods can be used. One is the
distributive method, one is the multiplication algorithm and most often
teachers use the FOIL method. FOIL is an acrostic for First, Outer, Inner
and Last in the product of binomials. My question is "who invented the FOIL
process of multiplying binomials? This process just did not happen, some
one must have come up with this simple process. Who?
There is nothing magic about the FOIL mnemonic for multiplying binomials.
There is no hidden math there, just a way for beginning students to keep the
various terms straight. Most students soon abandon its use because they
become so familiar with the multiplication process, it is no longer needed.
Probably "invented" by some old Greek sitting on a rock, drawing in the
I am not a professional mathematician, but I am a professional engineer.
In all of my years I have never heard of an inventor of a 'FOIL' method of
Perhaps it was Mr. Foil.
But if you look at both methods:
(A + B)(C + D)=
AC + BC + AD + BD
A + B
(X) C + D
BD + AD + BC + AC
Which is the same result as the FOIL method.
Substituting numbers in the binomials for A, B, C, D also results in the
same numeric value.
My educated estimate is that the FOIL method did not have a single inventor
who is forever ensconced on a pedestal in some internationally famous museum
for the rest of the history of time. I think somebody or even many people
simultaneously just figured this method out and it got written up in a text
book somewhere. Kind of like an old folk tale that becomes well known
throughout a population of people.
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Update: June 2012