How to Multiply Binomials

How to multiply binomials is perhaps one of the more difficult concept in the field of algebra. But when breaking this type of multiplication down into two steps, binomial multiplication becomes more clear. But first, let’s start with the basics.

The Basics
A binomial is an algebraic expression of the sum or the difference of two terms. For example:

(x + 3)  or
(x + 2)

Binomial multiplication is the mathematical method of how to multiply these binomials.  Using the two binomials introduced above we write binomial multiplication as follows:

(x + 3)(x + 2)

To know where we’re heading I am giving you the final answer already yet:

x² + 5x + 6

The Distributive Method
There are several methods of how to multiply binomials.  Here we discuss the “Distributive Method“.   This method is the most universal method and it applies even to all polynomial multiplications, not just to binomials.  In other words, the distributive method really useful stuff…..

Step 1
Find the first term in the first binomial; in our example this is x.  Multiply (distribute) this term times EACH of the terms in the second binomial (x + 2).  This goes as follows:

= x (x + 2)   [first term in the first binomial times EACH terms in the second binomial]

= x•x + x•2  [multiply]

= x² + 2x     [simplify]

Step 2
Now, take the second term in the first binomial, that is +3.  Notice we take the sign also. Multiply this term times EACH of the terms in the second binomial (x + 2).  In our example we get:

= 3•x +3•2  [multiply]

= 3x + 6     [simplify]

Finally, add up the intermediate results from step 1 and 2.

= step 1    +  step 2

= x² + 2x   +  3x + 6

= x² + 5x + 6

x² + 5x + 6 is our final result as given earlier. Can you see the “distributive property” at work?

(x + 3)(x + 2) = x(x + 2) + 3(x + 2).

If not then take a look at our video which visualizes the distributive method of multiplying binomials.

To learn other methods of how to multiply binomials such as FOIL or Area method or perhaps even multiplying of polynomials ask one of TutorZ’ algebra tutors.