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### 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:

(2x+3)(x-5)

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!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra

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