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Products of Binomials ("F OI L") and Trinomials Basic Algebra: One Step at a Time. Pages 123-126: F OI L Example;Page 131-132: #58, 61, 63.
Bittinger Section 4.4 p. 259: #35, 57
Dr. Robert J. Rapalje Altamonte Springs Campus Seminole State College of Florida Altamonte Springs, FL 32714
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 : =
Bittinger 4.4 p. 259: #35, 57
35.
By Distributive Property,
Remember that when you multiply with the same exponent, you must ADD exponents:
Reduce the fractions:
 57. 
I think it’s easier to multiply a binomial times a trinomial, so let’s begin by reversing the order of multiplication by the commutative property:
Now, from the binomial, multiply the
=
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