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### Multiplying Polynomials

```Date: 07/10/2003 at 00:19:46
From: Jalise
Subject: Foiling

(x+2)(x+2)(x+2)

How do you foil?
```

```
Date: 07/10/2003 at 12:21:22
From: Doctor Peterson
Subject: Re: Foiling

Hi, Jalise.

If you were told to use the FOIL method to do this, it won't work; it
applies only to the product of two binomials. To do this, you will
need a more general method for multiplying polynomials.

I'll demonstrate the process on a similar problem, so you can practice
with your own. We'll expand (x+3)(x+3)(x+3).

First, we have to multiply (x+3)(x+3), which we can do just as in
multiplying numbers: put one over the other, and multiply the top one
by each term of the other:

x + 3
*      x + 3
------------
3x + 9 <-- (x+3)3
x^2 + 3x     <-- (x+3)x
------------
x^2 + 6x + 9 <-- sum

So the first partial product, 3x + 9, is made by multiplying each term
of x + 3 by 3, and the second, x^2 + 3x, by multiplying each term of
x + 3 by x. We line them up so that like terms are in a column, and

Now we repeat, multiplying this by x + 3 again:

x^2 +   6x  + 9
*               x + 3
---------------------
3x^2 + 18x + 27 <-- (x^2 + 6x + 9)3
x^3 + 6x^2 +  9x      <-- (x^2 + 6x + 9)x
---------------------
x^3 + 9x^2 + 27x + 27

Do you see how easy it is to do this way? But it's just another trick
for multiplying every term of one polynomial by every term of the
other.

Here is a page with some explanation of why we prefer not to teach

Why FOIL?
http://mathforum.org/library/drmath/view/61769.html

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Polynomials

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