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### FOIL Procedure

```
Date: 8/13/96 at 22:20:31
From: Anonymous
Subject: FOIL Procedure

Hi!
I am having problems with the F.O.I.L concept. I understand the
procedure, it's just hard to remember. Got any hints? It is super
tough to learn the negatives and positives.

For example, how do I do (2X-5)(3Xsq-5x+4)?
```

```
Date: 8/14/96 at 0:43:33
From: Doctor Paul
Subject: Re: FOIL Procedure!

The idea of FOIL is to make sure that each term in the first set gets
multiplied by each term in the second set.  Let's do an example with
letters (not numbers).

(A + B) * (C -D + E)

We want to multiply each term in the second part (C, D, and E) by each
term in the first part (A, B)

The easiest way to go is just left to right.  Pick the leftmost term
in the first part (A) and multiply it by each successive term in the
second part.

We get:

A*C + A*(-D) + A*E

Then we add to this the next term in the first part times each of the
terms in the second part..

A*C + A*(-D) + A*E     + B*C + B*(-D) + B*(E)

When we add it all together, we get:

A*C - A*D + A*E + B*C - B*D + B*E

Get the idea?  Let's do a real example:

(2x-5)(3x^2-5x+4)

As seen above, we have:

2x*3x^2 + 2x*(-5x) + 2x*4 + (-5)*3x^2 + (-5)*(-5x) + (-5)*4

Let's multiply it out:

6x^3 - 10x^2 + 8x - 15x^2 + 25x - 20

Now we have two x^2 terms and two x terms. Let's combine them to get

6x^3 - 25x^2 + 33x - 20

I hope this helps you out.  If you have any more questions feel free
to submit them to Dr. Math.

Regards,

-Doctor Paul,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra

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