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You’ve now learned about FOIL = “First, Inner, Outer, Last”.
You may not believe this, but you have been using FOIL since you first learned to do
“long multiplication”.
Consider this:
You learned how to do this in grade school:
672
63
42
32
21
×
Now, this is from algebra:
(3x + 2)(2x + 1)
Foil tells us to do this:
F
O
I
L
6x
2
+ 3x
+ 4x
+ 2
Then we combine similar terms:
6x
2
+ 7x +2
Look at the two problems.
What do you notice?
Do you see any correlation between them?
What about if you were to replace x with 10, since our
number system is base 10?
What would the two polynomials in the “algebra” problem become?
Notice anything now?
Let me show the problems again and point out what I see:
21
x 32
42
63
672
(3x + 2)(2x + 1)
6x
2
+ 3x
+ 4x
+ 2
Then we combine similar terms:
6x
2
+ 7x +2
The coefficients of the polynomials match the
digits in the arithmetic problem
The coefficients in the FOIL expansion match
the digits in our long multiplication.
When we combine the similar terms, we are
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 Spring '09
 RANJITREBELLO

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