The LessonThe FOIL stands for the First Outside Inside Last method. The FOIL method is a method for multiplying two brackets together. Two brackets multiplying each other are shown below:
Each of the brackets (a + b) and (c + d) have two terms added (or subtracted) to each other. They are called binomials because they each have two terms. The FOIL method gives the order to multiply the terms together:
How to Use the FOIL MethodUsing the FOIL method to expand two brackets is easy. Just remember First Outside Inside Last.
QuestionExpand the brackets below.
First: Multiply the first terms in each of the brackets together.
x × x = x2 x2
Outside: Multiply the outside terms in each of the brackets together, and add to the previous result.
x × 2 = 2x x2 + 2x
Inside: Multiply the inside terms in each of the brackets together, and add to the previous result.
1 × x = x x2 + 2x + x
Last: Multiply the last terms in each of the brackets together, and add to the previous result.
1 × 2 = 2 x2 + 2x + x + 2
Simplify the expression if necessary by collecting like terms together. In our example, we can collect the x terms together.
x2 + 2x + x + 2 = x2 + 3x + 2
Answer:We have used the FOIL method to expand the expression:
Lesson SlidesThe slider below shows another real example of using the FOIL method. Open the slider in a new tab
Multiplying a number with a variable.
2 × x = 2x 5 × x = 5x
Multiplying a number with a variable with a coefficient.
2 × 2x = 4x 3 × 5x = 15x
Multiplying a variable with a variable.
x × y = xy x × x = x2
Multiplying a variable with a variable with a coefficient.
x × 2y = 2xy 3x × x = 3x2
Multiplying two variables with coefficients together.
2x × 3y = 6xy 3x × 5x = 15x2
The FOIL Method and FactoringIn the example on this page, two brackets containing x's are multiplied together.
(x + 1)(x + 2)Using the FOIL method results in a quadratic equation:
x2 + 3x + 2This suggests that if the reverse process takes place, some quadratic equations can be written as two brackets mulitplied together:
(x + a)(x + b)This is known as factoring a quadratic equation, and is of great help when solving quadratic equations.