Using FOIL to Solve Algebraic Equations

High School Student Reviewing Algebra Equations Digital Tablet

Hero Images/Getty Images 

Early algebra requires working with polynomials and the four operations. One acronym to help multiply binomials is FOIL. FOIL stands for First Outer Inside Last.


  • (4x + 6) (x + 3)

We look at the first binomials which are 4x and x which gives us 4x2

Now we look at the two outside binomials which are 4x and 3 which gives us 12x

Now we look at the two inside binomials which are 6 and x whichh gives us 6x

Now we look at the last two binomials which are 6 and 3 which gives us 18

Finally, you add all of them together to get: 4x2 +18x + 18

All you need to remember is what FOIL stands for, whether you have fractions involved or not, just repeat the steps in FOIL and you will be able to mulitply to binomials. Practice with the worksheets and in no time it will come to you with ease. You are really just distributing both terms of one binomial by both terms of the other binomial.


Here are 2 PDF worksheets with answers for you to work on to practice multiplying binomials using the FOIL method. There are also many calculators that will do these calculations for you, but it is crucial you understand how to multiply binomials correctly before using calculators. You will need to print the PDFs to see the answers or practice with the worksheets.

Also, here are 10 sample questions to practice with:

  1. (4x - 5) (x - 3)
  2. (4x - 4 (x - 4)
  3. (2x +2) (3x + 5)
  4. (4x - 2) (3x + 3)
  5. (x - 1) (2x + 5)
  6. (5x + 2) (4x + 4)
  7. (3x - 3) (x - 2)
  8. (4x + 1) 3x + 2)
  9. (5x + 3) 3x + 4)
  10. (3x - 3) (3x + 2)


It should be noted that FOIL can only be used for binomial multiplication. FOIL is not the only method that can be used. There are other methods, although FOIL tends to be the most popular. If using the FOIL method is confusing for you, you may wish to try the distributive method, the vertical method or the grid method. Regardless of the strategy, you find to work for you, all the methods will lead you to the correct answer. After all, mathematics is about finding and using the most efficient method that works for you.

Working with binomials usually occurs in the ninth or tenth grades in high school. An understanding of variables, multiplication, binomials are required before multiplying binomials. 

mla apa chicago
Your Citation
Russell, Deb. "Using FOIL to Solve Algebraic Equations." ThoughtCo, Apr. 5, 2023, Russell, Deb. (2023, April 5). Using FOIL to Solve Algebraic Equations. Retrieved from Russell, Deb. "Using FOIL to Solve Algebraic Equations." ThoughtCo. (accessed June 6, 2023).