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
   

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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