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Appendix B

The FOIL Method

 

 

Definitions

   

Monomial

An algebraic expression which is either a constant or a product of constants and variables. *

Polynomial

The sum of one or more monomials. *

Binomial

A polynomial which contains two monomials.

Trinomial

A polynomial which contains three monomials.

Term

An algebraic expression all of whose parts are connected by multiplication (and/or division). *

 

We square a binomial by multiplying it by itself. An easy way to remember how to do this is the FOIL method. The acronym, FOIL, means First Outer Inner Last.

In this example, we have .

We can write this as.

Multiply the First terms that appear in each binomial (75 and 75); we get 5625.

Next, multiply the Outer terms in each binomial (75 and ); we get .

Now, multiply the Inner terms in each binomial ( and 75); we get .

Finally, multiply the Last terms in each binomial ; we get .

Now we add the like-terms of the resulting polynomial

The like terms are and .

This yields .

Now we add all the terms together (and arrange the terms in standard order) to get our final trinomial, ().

The FOIL Method

 

 

Copyright 1998 by Andrew S. Rich. All rights reserved.

 

* Goodman, Arthur, and Hirsch, Lewis. Understanding Elementary Algebra. Third ed. St. Paul: West Pub. Co., 1994

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