From: Jeanne (for Teacher2Teacher Service)
Date: Nov 16, 2000 at 00:07:44
Subject: Re: FOIL Method of multiplying polynomials

Hello Angela,

I use an area model to teach the multiplication of polynomials.  We start
with (length)(width) = area of a rectangle.

Depending upon the class we might start with something as basic as (12)(34).
     (12)(34) = (10 + 2)(30 + 4)  We use the (10 + 2) and the (30 + 4) as the
length and width, respectively.

      __30__+___4__                             __30__+___4__
     |      |      |   The area of each        |      |      |
   10|      |      |   rectangle is computed 10| 300  |  40  |
    +|______|______|   separately.            +|______|______|
     |      |      |                           |      |      |
    2|      |      |                          2|  60  |  8   |
     |______|______|                           |______|______|

The total area is 300 + 40 + 60 + 8 or 408.

Applying this to polynomials...

      __x___+___4__                             __x___+___4__
     |      |      |   The area of each        |      |      |
    x|      |      |   rectangle is computed  x| x^2  |  4x  |
    +|______|______|   separately.            +|______|______|
     |      |      |                           |      |      |
    2|      |      |                          2|  2x  |  8   |
     |______|______|                           |______|______|

The total area is x^2 + 4x + 2x + 8 or x^2 + 6x + 8.

Hope this helps.

 -Jeanne, for the T2T service