# FOIL Method

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

 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

ProductFirstOuterInnerLastResult
(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. 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
2. 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
3. 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

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.

### 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.)