Multiplying Binomials Using the FOIL Method
FOIL can be used to multiply any two binomials. The binomials
in the next example have powers higher than 1.
Example 1
Using the FOIL method
Find each product.
a) (x^{3}  3)(x^{3} + 6)
b) (2a^{2} + 1)(a^{2} + 5)
Solution
a) (x^{3}  3)(x^{3} + 6) 
= x^{6} + 6x^{3}  3x^{3}
 18 

= x^{6} + 3x^{3}  18 
b) (2a^{2} + 1)(a^{2} + 5) 
= 2a^{4} + 10a^{2} + a^{2}
+ 5 

= 2a^{4} + 1a^{2} + 5 
Multiplying Binomials Quickly
The outer and inner products in the FOIL method are often like terms, and we
can combine them without writing them doun. Once you become proficient at using
FOIL, you can find the product of two binomials without writing anything except
the answer.
Example 2
Using FOIL to find a product quickly
Find each product. Write down only the answer.
a) (x + 3)(x + 4)
b) (2x  1)(x + 5)
c) (a  6)(a + 6)
Solution
a) (x + 3)(x + 4) = x^{2} + 7x + 12 
Combine like terms: 3x + 4x = 7x. 
b) (2x  1)(x + 5) = 2x^{2} + 9x  5 
Combine like terms:10x  x = 9x. 
c) (a  6)(a + 6) = a^{2}  36 
Combine like terms: 6a  6a = 0 