The FOIL Method

In this lesson, we will look into how to use the FOIL method to distribute two binomials.

Most Algebra books describe FOIL as a method of multiplying two binomials.
FOIL is the acronym for
First
Outside
Inside
Last

Example:

Multiply the binomials (x + 1)(2x – 3)

Solution:

(x + 1)(2x – 3)

Multiply First : x • 2x = 2 x²
Multiply Outside : x • (–3) = –3x
Multiply Inside : 1 • 2x = 2x
Multiply Last : 1 • (–3) = –3

(x + 1)(2x – 3)
= 2x² – 3x + 2x – 3
= 2x² – x – 3

The following diagram shows how to use the FOIL method to distribute or multiply two binomials. Scroll down the page for more examples and solutions.

 

Important Notes:

• The FOIL method only works for multiplying two binomials. For more complex expressions, use the distributive property.
  
• After using FOIL, always check if you can simplify the resulting expression by combining like terms.
  

Algebra Worksheets
Practice your Algebra with the worksheets.
Printable & Online Algebra Worksheets

Multiplying Binomials FOIL Method
Multiplying binomials using the FOIL method. Explanation and examples.
(a + 3)(a + 7)
(x + 3)(x - 5)
(2x + 4)(3x + 5)

How to Use Foil to Distribute Two Binomials?
This video will show you how to use foil to distribute two binomials.
(x + 3)(x + 2)
(x + 4)(x - 5)
(x - 2)(x - 6)

• Show Video

FOIL Method for Multiplying Binomials - Distributive Property
In this video, we use the FOIL method to multiple binomials. FOIL helps you make sure all terms are distributed. (a+b)(c+d)
(x + 2)(3x - 7)

• Show Step-by-step Solutions

Practice Problems

1. Multiply (x+4)(x+5)
   Solution:
   (x+4)(x+5)= x² + 5x + 4x + 20 = x² + 9x + 20
   
2. Multiply (2x−3)(x+7)
   Solution:
   (2x−3)(x+7)=2x² + 14x − 3x − 21 = 2x² + 11x − 21
   
3. Multiply (3y+2)(y−4)
   Solution:
   (3y+2)(y−4)=3y² − 12y + 2y − 8 = 3y² − 10y − 8
   

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