The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Expand Binomial

Date: 6/13/96 at 12:36:13
From: Anonymous
Subject: Expand binomial

Hi! I'm from R. H. Dana and I want to ask you a question.

Expand:  (2x + 3)(x - 5)

Date: 6/13/96 at 21:27:6
From: Doctor Paul
Subject: Re: Expand binomial

Let's talk about how to do this problem in the general case and then 
we'll do it in your specific case. 

When asked to expand a problem like:
(A + B)(C + D) 

there is a procedure to follow...
Step One:    Multiply A and C
Step Two:    Multiply A and D;  Then add this to step one
Step Three:  Multiply B and C;  Then add this to step two
Step  Four:  Multiply B and D;  Then add this to step three.

You would end up with A*C + A*D + B*C + B*D

Now let's do your specific case of:


Step One: 2x*x = 2x^2

Step Two: 2x*(-5) = -10x
   Now add -10x to step one:  2x^2 - 10x

Step Three: 3*x = 3x
   Now add 3x to step two:  2x^2 - 10x + 3x

Step Four:  3*(-5) = -15
   Now add -15 to step three:  2x^2 - 10x + 3x - 15

Finally, simplify step four:

2x^2 - 7x - 15

-Doctor Paul,  The Math Forum
 Check out our web site!   
Associated Topics:
Middle School Algebra

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.