FOIL Method

Pronunciation: /fɔɪl ˈmɛθ əd/ ?

Figure 1: Foil method.

The FOIL method is an algorithm for expanding the product of two binomials. FOIL is an acronym that stands for First, Outer, Inner, Last.

Examples

Product	First	Outer	Inner	Last	Result
(x+1)(x-1)	x·x = x2	x·(-1) = -x	1·x = x	1·(-1) = -1	x2 + (1-1)x + (-1) = x2 - 1
(x-3)(x-2)	x·x = x2	x·(-2) = -2x	(-3)·x = -3x	(-3)·(-2) = 6	x2 + (-2-3)x + 6 = x2 - 5x + 6
(2x+1)(3x+2)	2x·3x = 6x2	2x·2 = 4x	1·3x = 3x	1·2 = 2	6x2 + (4+3)x + 2 = 6x2 + 7x + 2
Table 1

References

1. Kay Thompson. Algebra and Trigonometry Structure and Method: Book 2, pp 174-175. Mcdougal Littell/Houghton Mifflin, April 1994.
2. Douglas K. Brumbaugh, Peggy L. Moch, and MaryE Wilkinson. Mathematics Content for Elementary Teachers , pp 64-66. Routledge, August 2004.

More Information

• How to Use FOIL to Distribute Two Binomials (video). dummies.com. Wiley. 2010-01-23. http://www.dummies.com/how-to/content/how-to-use-foil-to-distribute-two-binomials.html.

Printed Resources

Cite this article as:

FOIL Method. 2010-02-05. All Math Words Encyclopedia. Life is a Story Problem.org. http://www.allmathwords.org/en/f/foilmethod.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem.org and are licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Revision History

2010-02-05: Added "References" (McAdams, David.)
2009-01-03: Initial version (McAdams, David.)