FOIL Method

Pronunciation: /fɔɪl ˈmɛθ əd/ ?

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.


(x+1)(x-1)x·x = x2x·(-1) = -x1·x = x1·(-1) = -1x2 + (1-1)x + (-1)
= x2 - 1
(x-3)(x-2)x·x = x2x·(-2) = -2x(-3)·x = -3x(-3)·(-2) = 6x2 + (-2-3)x + 6
= x2 - 5x + 6
(2x+1)(3x+2)2x·3x = 6x22x·2 = 4x1·3x = 3x1·2 = 26x2 + (4+3)x + 2
= 6x2 + 7x + 2
Table 1


  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

Printed Resources

Cite this article as:

FOIL Method. 2010-02-05. All Math Words Encyclopedia. Life is a Story Problem LLC.

Image Credits

Revision History

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

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License