Using the â€œFOILâ€ Method to Multiply Two Binomials
To multiply a binomial by a binomial, we use the Distributive Property
twice.
For example, letâ€™s multiply (a + b)(c + d).
Distribute (c + d) to both a and b. 
(a + b)(c + d) = a(c + d) + b(c + d) 
Distribute both a and b to
each term in (c + d). 
= ac + ad + bc + bd 
Notice that each term in (a + b) has been
multiplied by each term in (c + d).
To remember how to multiply two binomials, we use the word FOIL.
FOIL stands for First, Outer, Inner, Last.
â€¢ The product of the First terms is ac.
â€¢ The product of the Outer terms is ad.
â€¢ The product of the Inner terms is bc.
â€¢ The product of the Last terms is bd.
Note:
This picture may help you remember how
to use the FOIL method. The arcs form a
â€œface.â€
Example 1
Find: (x  2)(x + 5)
Solution 

F 

O 

I 

L 
Use FOIL. Simplify each product.
Combine like terms. 
(x  2)(x + 5) = =
= 
(x)(x) x^{2}
x^{2} 
+ +
+ 
(x)(5) 5x

+ 
3x 
(2)(x) 2x

+ 
 
(2)(5) 10
10 
So, (x  2)(x + 5) = x^{2} + 3x  10.
Example 2
Find: (3w  7)(9w  5)
Solution 

F 

O 

I 

L 
Use FOIL. Simplify each product. Combine like terms. 
(3w  7)(9w  5) = =
= 
(3w)(9w) 27w^{2}
27w^{2} 
+ 
 
(3w)(5) 15w

+ 
78w 
(7)(9w) 63w

+ +
+ 
(7)(5) 35
35 
So, (3w  7)(9w  5) = 27w^{2}  78w + 35.
