FOIL Method

Pronunciation: /fɔɪl ˈmɛθ.əd/ Explain
Abbreviation: FOIL Method

In (ax+b)(cx+d) the first terms of the binomials are ax and cx, their product is acx^2. The outer terms are ax and d, their product is adx. The inner terms are b and cx, their product is bcx. The last terms are b and d, their product is bd. The product (ax+b)(cx+d)=acx^2+(ad+bc)x+bd.

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` = `x`²	`x` · (-1) = ^-`x`	1 · `x` = `x`	1 · (-1) = -1	`x`² + (1-1)`x` + (-1) = `x`² - 1
(`x` - 3)(`x` - 2)	`x` · `x` = `x`²	`x` · (-2)\ = -2`x`	(-3) · `x` = -3`x`	(-3) · (-2) = 6	`x`² + (-2 - 3)`x` + 6 = `x`² - 5`x` + 6
(2`x` + 1)(3`x` + 2)	2`x` · 3`x` = 6`x`²	2`x` · 2 = 4`x`	1 · 3`x` = 3`x`	1 · 2 = 2	6`x`² + (4 + 3)`x` + 2 = 6`x`² + 7`x` + 2
Table 1

References

McAdams, David E.. All Math Words Dictionary, foil method. 2nd Classroom edition 20150108-4799968. pg 81. Life is a Story Problem LLC. January 8, 2015. Buy the book
Kay Thompson. Algebra and Trigonometry Structure and Method: Book 2. pp 174-175. Mcdougal Littell/Houghton Mifflin. April 1994. Last Accessed 7/11/2018. Buy the book
Douglas K. Brumbaugh, Peggy L. Moch, and MaryE Wilkinson. Mathematics Content for Elementary Teachers. pp 64-66. Routledge. August 2004. Last Accessed 7/11/2018. Buy the book

More Information

How to Use FOIL to Distribute Two Binomials (video). dummies.com. Wiley. 1/23/2010. http://www.dummies.com/how-to/content/how-to-use-foil-to-distribute-two-binomials.html.

Cite this article as:

McAdams, David E. FOIL Method. 4/21/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://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 LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/21/2019: Modified equations and expression to match the new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/9/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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