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Q&A #5112


FOIL Method of multiplying polynomials

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From: Pat Ballew (for Teacher2Teacher Service)
Date: Nov 15, 2000 at 00:53:31
Subject: Re: FOIL Method of multiplying polynomials

FOIL is so often used that it seems to be trying to sweep back the tide, but
I continue to try to tell teachers that it probably is NOT a good idea to
introduce a new memory for an old idea that students mostly understand. FOIL
is just a limited case of the distributive property that is used in everyday
multiplication by almost all students in the conventional multiplication
algorithm. But many of them do not understand what they do when they use it.

My suggestion: start by teaching them the inside story about 23*34 in
traditional form, but do it by writing 23 as 20+3, and 34 as 30+4... then the
old algorithm (with NO regrouping until the addition looks like this:

             20 + 3
             30 + 4
_______________________
                  12


then
             20 + 3
             30 + 4
_______________________
             80 + 12

then
             20 + 3
             30 + 4
_______________________
             80 + 12
             90           being on the next line is not essential, just a
shortcut to make life easy

and then
             20 + 3
             30 + 4
_______________________
             80 + 12
       600 + 90

And now we add 600 + 170 + 12 to get 782.

With polynomials it gets even easier because we don't have to do some of the
regrouping.  We can replace the ten's with a variable and we have 2x+3 (3x+4)
             2x + 3
             3x + 4
_______________________
             8x + 12
      6x^2 + 9x
     and combining like terms we get 6x^2 + 17x + 12

With FOIL, you have reached a dead end as soon as you get to this point, but
with the basic multiplication model you can move quickly into binomial times
trinomial or any polynomial times any other without concern about the degree.
At the end, students will understand the basic algorithm better than they did
when they started, and also have no fear of multiplying polynomials... it's
just another use of an old familiar tool...

Hope that helps, good luck

 -Pat Ballew, for the T2T service

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