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
+ a2 + ab  
  a2 + ab - ac - bc
  a2 + a(b - c) - bc