Multiplying Binomials
In this section you will learn a rule that makes multiplication of binomials
simpler.
The FOIL Method
We can use the distributive property to find the product of two binomials.
For example,

= (x + 2)x + (x + 2)3 
Distributive property 

= x^{2} + 2x + 3x + 6 
Distributive property 

= x^{2} + 5x + 6 
Combine like terms 
There are four terms in x^{2} + 2x + 3x + 6.
The term x^{2} is the product of the first
terms of each binomial, x and x. The term 3x is the product of the two outer
terms, 3 and x. The term 2x is the product of the two inner terms, 2
and x. The term 6 is the product of the last term of each binomial, 2 and
3. We can connect the terms multiplied by lines as follows:

F = First terms
O = Outer terms
I = Inner terms
L = Last terms 
If you remember the word FOIL, you can get the product of the
two binomials much faster than writing out all of the steps above. This method
is called the FOIL method. The name should make it easier to remember.
Example 1:
Using the FOIL method
Find each product.
a) (x + 2)(x  4)
b) (2x + 5)(3x  4)
c) (a  b)(2a  b)
d) (x + 3)(y + 5)
Solution
a)

Combine the like terms 
b) (2x + 5)(3x  4) 
= 6x^{2}  8x + 15x  20 


= 6x^{2} + 7x  20 
Combine the like terms 
c) (a  b)(2a  b) 
= 2a^{2}  ab 2ab + b^{2} 


= 2a^{2}  3ab + b^{2} 
Combine the like terms 
d) (x + 3)(y + 5) 
= xy + 5x + 3y + 15 
There are no like terms to combine. 
