FOIL Method


You will find a lot of questions on mathematics exams that rely on FOIL method. FOIL is a subset of algebra and is related to polynomials. Unlike many other algebra sections, you cannot only rely on plugging in. Though it’s a method that can effectively help you out on a number of questions.

Before moving on the use of FOIL, the foremost thing is to know about the polynomials. Look at the following equation:

(x – y) (x + y) = 0

Keep in mind that parentheses stand for multiplication. Though multiplying x and y may seem difficult to you but with the FOIL method, we can make things pretty easy and quick.

Now think of the position of the x’s and y’s in the above equation. The first position in each parenthesis will consists of x’s. Whereas the last position will consist of y’s. Using this logic, we will apply the FOIL method.

F: First, x2

O: Outer, xy

I: Inner, -xy

L: Last, y2

Now think that the above variables are a part of large addition problem.

x+ xy – xy – y2 = 0

x– y2 = 0

Now let’s practice it.

(x + 2) (x – 4) = 0

F: x2

O: -4x

I: 2x

L: -8

x– 2x – 8 = 0

Also, you can reverse the direction in which you do FOIL such as:

x– 4x + 4 = 0

First, you need to set up the parentheses.

(x -?) (x -?) = 0

The question marks in the above equation are in the last position. We will multiply them together, we get 4. Notice that the +4 is at the end of equation. Hence, we know that the last numbers i.e. the question marks, when multiplied will be equal to +4.

Also, note that the -4x is in the middle of the equation. The outer is

(X x ?) + (X x ? ) = -4x

Which two numbers when multiplied will be equal to +4 and when added will be equal to -4. You may need to work on factors a little but as only factors of 4 are 2, 2 and 4, 1, so this problem is not so tough. You can easily add 4 and 1, you will get 5. Hence 2 and 2 are the right answers and now we can replace the question marks with 2’s thus giving us

(x – 2) (x – 2) = 0

Let’s try another question:

Find the root of the equation 2x2 – 20x = 48

A -5

B 2

C 6

D 10

E 12



2x2 – 20x = 48

2x2 – 20x – 48 = 0

2 (x – 10x -24) = 0

2 (x-12) (x+12) = 0

x – 12= 0

x = 12

x + 2 = 0

x = -2

So, the right answer is E.

Once you get to know the FOIL method, you will remember it throughout your life and especially on your test day.

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