Online College Courses for Credit

3 Tutorials that teach Using FOIL to Represent Area
Take your pick:
Using FOIL to Represent Area

Using FOIL to Represent Area

Author: Sophia Tutorial

This lesson covers using FOIL to represent area.

See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

Begin Free Trial
No credit card required

29 Sophia partners guarantee credit transfer.

311 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 27 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.


What's Covered

  • Representing Area with Binomial Multiplication
  • Subtracting Area with Binomial Multiplication

Using FOIL to Represent Area

Representing Area with Binomial Multiplication

In the image below, we see a floor plan of an office space.  In the office, there is the main section with workspaces and cubicles, a kitchenette, a break room, and a bathroom:

Note that we know some measurements of the areas in the office, while other measurements are unknown.  Adding the partial dimensions together, we can express the area of the entire office using binomial multiplication. 

The area of the room can be expressed as: (x + 8)(x + 5)

We can expand binomial multiplication using a process known as FOIL. FOIL stands for First, Outside, Inside, Last, and is used as an aid in remembering which terms to multiply together to expand two binomials being multiplied together.

Using FOIL, we see that we can equivalently express the area as:

Notice that when we express the area using 4 terms, each term represents the area of the individual sections to the office:

  • The bathroom has an area of x2 square feet
  • The kitchenette has an area of 8x square feet
  • The break room has an area of 5x square feet
  • The main work room has an area of 40 square feet


We can, and should, further simplify the area by combining like terms: x2 + 13x + 40

Subtracting Area with Binomial Multiplication

At a different office space, workers are coming in to install carpeting on the floor.  However, they need to leave a boarder of wooden floor around the office for certain equipment.  The floor plan is illustrated below:

We can represent the area of the carpet using binomial multiplication as well. However, our binomials will include subtraction, because we need to take away from the dimension of the office space. 

The area of the carpet can be expressed  as: (12 – 2x)(10 – 2x)


We subtract 2x in this case, because a distance of x feet is being trimmed from both sides of the length and width of the room. 

Using FOIL, we can equivalently express the area as a polynomial in expanded form.  This is illustrated below: