FOIL Method

Pronunciation: /fɔɪl ˈmɛθ əd/ Explain

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. Buy the book
  2. Douglas K. Brumbaugh, Peggy L. Moch, and MaryE Wilkinson. Mathematics Content for Elementary Teachers. pp 64-66. Routledge. August 2004. Buy the book

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Cite this article as:

McAdams, David E. FOIL Method. 7/11/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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7/9/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)

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