1. Multiplying Binomials
Ye Olde FOIL Method
Multiplying Binomials
Welcome to the Verde Learning Center Tutorial on the Foil Method for Multiplying Binomials

2. FOIL Method – Multiplying Binomials
Arrg - What’s a binomial?
A binomial is a algebraic expression that has 2 terms
Each term will contain numbers and or variables(letters)
The terms are separated by addition or subtraction signs
X + 7 is a binomial
Here are some other binomial examples
3 + y
x - y
2x + 1
10 + 1
What’s a binomial? A binomial is an algebraic expression that has 2 terms. Each term will contain numbers and or variables (which are letters). The terms are separated by addition or subtraction signs. X + 7 is a binomial.

3. Foil Method – Multiplying Binomials
What not to do - A common mistake
Students frequently try to multiply only the first and last terms of the binomial. This is only part of the answer.
(a + b)
(a + b)
= a2 + b2
Here’s a common mistake.

4. FOIL Method – Multiplying Binomials
A common mistake
(10 + 1)
(10 + 1) =
= = 101
Let’s substitute numbers and check. Only multiply the first and last terms gives us a result of However 10+1 is 11 and 11 x 11 is 121 so we can see there is something wrong with this method
(10 + 1)
(10 + 1)
= (11) (11) = 121
Since we know that 10+1 is 11 and 11 times 11 is 121 we can see that something is wrong with this method

5. FOIL Method – Multiplying Binomials
Time to break out the Mystery FOIL
Time to break out the mystery foil.

6. FOIL Method – Multiplying Binomials
FOIL stands for
First
Outside
Inside
Last
(10 + 1)
(10 + 1)
= 10 10 + 10 1 + 1 10 + 1 1 * * * *
= 100
+ 10
+ 10
+ 1
= 121
FOIL stands for First Outside Inside and Last We will multiply the first terms of each binomial, then the terms on the outside, then the inside terms, and finally the last terms. This results in 121 which is the correct answer. Foil is a great method for multiplying binomials.
(10 + 1)
(10 + 1)
= (11) (11) = 121
This is a great method for multiplying binomials

7. FOIL Method – Multiplying Binomials
Ye other example:
First
Outside
Inside
Last
(x + 3)
(x + 4)
= x x + x 4 + 3 x + 3 4 * * * *
= x2
+ 4x
+ 3x
+ 12
Combine the like terms.
+ 7x
= x2 + 7x +12

8. FOIL Method – Multiplying Binomials
Here’s the please show me another example:
First
Outside
Inside
Last
(x + y)
(x + y)
= x x + x y + x y + y y * * * *
= x2
+ xy
+ xy
+ y2
Here is another example. We will multiply x +y and x+y. when we multiply the first terms we have x*x when we multiply the outside terms we have x*y when we multiply the inside terms we have x*y and the last terms result in y*y
Simplifying we have x squared plus xy plus xy plus y squared
Combining the like terms we have x squared plus 2xy plus y squared
Combine the like terms.
+ 2xy
= x2 + 2xy + y2

9. FOIL Method – Multiplying Binomials
Another olde example:
First
Outside
Inside
Last
(x + 2)
(x - 3)
= x x + x -3 + 2 x + 2 -3 * * * *
= x2
+ -3x
+ 2x
+ -6
Here is last example. When there is subtraction in a binomial, we treat the subtraction sign as if it were attached to the number so in the binomial x – 3 we will have an x term and a negative 3 term.
In this example, we will multiply x +2 and x-3. multiplying the first terms we have x*x when we multiply the outside terms we have x*-3 when we multiply the inside terms we have 2*x and the last terms result in 2*-3
Simplifying we have x squared plus -3x plus 2x plus -6
Combining the like terms we have x squared plus -x plus -6
Adding a negative number is the same as subtract that number so we further simplify and write
X squared minus x minus 6
Don’t forget the negative sign! -x
= x2 -x -6

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Ye Olde FOIL Method
Tutorial
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