5.5 The Product of Two Binomials
A binomial is a mathematical expression containing two terms.
There are four different types of products for binomials. We begin with number and write them then with variables:
A. (3 + 4) (3  5)
B. (3  4) (3  5)
C. (3  4) (3 + 5)
D. (3 + 4) (3 + 5)
Note that all the pairs of factors have a common term, in other words 3.


We do the first multiplication: 



3 
+ 
4 




· 
3 
 
5 









20 




 15 



+ 
9 
+12 







9 
 3 
 20 
=  14 

Check that it is correct:
(3 + 4) = 7
(3  5) = 2
7 · (2) =  14
It is correct!


We will try to do an example with an algebraic expression, and we will replace the constant terms with variables, 3 with 1, 4 with b, and 5 with c. 



a 
+ 
b 




· 
a 
 
c 








 ac 
 bc 


+ 
a^{2} 
+ ab 







a^{2 }+ ab  ac 
 bc 



a^{2} + a(b  c) 
 bc 


