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Name: Duane
Status: educator
Grade: 9-12
Location: SC
Country: USA
Date: N/A 

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 sand.

Vince Calder

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 binomial multiplication.

Perhaps it was Mr. Foil.

But if you look at both methods:

FOIL Method:
(A + B)(C + D)=

AC + BC + AD + BD

Distribution Method:
A + B (X) C + D

Results in

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.

Sincere regards,
Mike Stewart

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