Products of Binomials
"F
OI
L"
Basic
Algebra: One Step at a Time. Pages
123-126: F
OI
L Example;
Page 131-132: #58, 61, 63.
Dr. Robert J. Rapalje
Seminole Community College
Sanford, FL 32773
To see
Section 2.01, with
detailed explanations, examples, exercises, and answers,
click here!
F = First times First
O = Outer times Outer
I = Inner times Inner
L = Last times Last
P
roducts
of Binomials “F
OI
L”
F
O
I
L
Example 1.
(x + 4) (x
+ 3) = x2
+ 3x + 4x
+ 12
=
x2
+ 7x
+ 12
F
O I
L
Example 2.
(x + 6) (x
+ 4) = x2
+ 4x + 6x
+ 24
= x2
+ 10x
+ 24
P. 131 #58.
Solution:
This is a
trinomial times a
trinomial!! You
must multiply the first term
in the first parentheses times the
second parentheses,
the second term
times the second
parentheses, and the
third term times the
second parentheses,
as indicated in the color coordinated scheme below:
P. 132 #61.
Solution: Of course you realize this means:
.
In math, everything is “binary.” That is, if you have three numbers to be
multiplied, you must multiply two together first, and then multiply that
product times the third number. It does not matter in what order you
perform the multiplications. It might be convenient to multiply the second
two together (by F
O I L)
first, like this:
Now, you can treat this as a product of a binomial times a trinomial, as the
following colors indicate. Multiply the
first times everything in the
second parentheses, the
second times
everything in the second parentheses.
First:
= 
Second:
Finally, combine like terms : =
P. 132 #63.
Solution:
Of course you realize this means:
.
In math, everything is “binary.” That is, if you have three numbers to be
multiplied, you must multiply two together first, and then multiply that
product times the third number. It does not matter in what order you
perform the multiplications. It might be convenient to multiply the second
two together (by F
O I L)
first, like this:
Now, you can treat this as a product of a binomial times a trinomial, as the
following colors indicate. Multiply the
first times everything in the
second parentheses,
the second times
everything in the second parentheses.
First:
=
Second:
Finally, combine like terms : =
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C
O
L O
R
!!
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