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Polynomial
Multiplication
Copyright©1999 Lynda Greene
The FOIL
Multiplication
Method
FOIL is a method used to
multiply two binomials, such as:
(x + 3)(x - 2)
binomial: two terms
Foil has only one use, if there are
more than two terms a different
method must be used.
Example: (x - 2)(x2 + 2x -3) cannot use FOIL
Three terms: Trinomial
FOIL is an acronym, meaning
each letter stands for a word.
O: stands for
F: stands for
the First terms
the outer terms
(x + y)(a - 2b)
I: stands for the
inner terms
L: stands for
the last terms
FOIL is the order we use to multiply these expressions
F:first times first
O
F
O:outer times outer
(x + y)(a - 2b)
I:Inner times Inner
I
L
L: last times last
ax - 2bx + ay - 2by
It is customary to write the letters (variables) in each
term in alphabetical order and to write the number
(coefficient) in front.
6
F:first times first
O
F
O:outer times outer
(2x + 3)(x + 2)
I:Inner times Inner
2
2x
I
L
L: last times last
+ 4x + 3x + 6
Very often the two middle terms are “like terms” and
can be combined. 4x + 3x = 7x
Answer: 2x2 + 7x + 6
7
F:first times first
O
F
O:outer times outer
(3x - 4)(2x + 1)
I:Inner times Inner
2
6x
I
L
L: last times last
+ 3x - 8x - 4
Very often the two middle terms are “like terms” and
can be combined. 3x - 8x = -5x
Answer: 6x2 - 5x - 4
8
F:first times first
O
F
O:outer times outer
(x - 6) (x + 6)
I:Inner times Inner
2
x
I
L
L: last times last
+ 6x - 6x - 36
The answer to this kind of problem is called
“the difference of two squares”
The middle term always cancels out (6x – 6x = 0)
Answer: x2 - 36
9
FOIL Practice Problems: (Hit enter to see the answers)
1) (x + 7)(x – 3)
2) (x – 2)(x – 5)
3) (x + 2y)(3x + y)
4) (x + 3)(x – 3)
5) (2 + x)(3 + x)
Answers:
1) x2 + 4x – 21
2) x2 – 7x + 10
3) 3x2 + 7xy + 2y2
4) x2 - 9
5) 6 + 5x + x2
End of Tutorial
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