Multiplying Polynomials
Be able to use different
methods to multiply two
polynomials.
Multiplying Polynomials
• To multiply polynomials together each term
of the first polynomial must be multiplied
by each term of the second polynomial.
• There are several methods for multiplying
polynomials.
• The three methods we will be using are the
box method, using the memory device
FOIL, and using the distributive property.
FHS
Polynomials
2
The Box Method
• The simplest method for multiplying
polynomials is to use a box or a chart to
fill in. Here is an example:
5
53x
44
2x 
3x 
2x
6x
2
8x
FHS
15x
6 x 2  15 x  8 x  20
20
6 x 2  7 x  20
Polynomials
3
How does FOIL work?
• Look at the example below to show FOIL at work:
F = multiply the first term in each binomial
O = multiply the two outside terms together
I = multiply the two inside terms together
L = multiply the last term in each binomial
6 2x +3)
3
(xx + 6)(2x
· + ·
+ · + ·
= 2x2 + 3x + 12x + 18 = 2x2 + 15x + 18
FHS
Polynomials
4
The Distributive Method
• The third method is to use the distributive
property to multiply each term of the first
polynomial by each term of the second
polynomial. You must use this method or the
box method if you are multiplying polynomials
that are not binomials.
2
2
2

3
x
x

2
x

4

5
x
 2x  4
 3x  5 x  2 x  4



 

 3x3  6 x 2  12 x  5 x 2  10 x  20
 3x  11x  22 x  20
3
FHS
Polynomials
2
5
Let’s Practice
1. (y – 5)(y – 1) =
y2 – y – 5y + 5 =
y2 – 6y + 5
3. (5 – x)(5 + x) =
25 + 5x – 5x – x2 =
25 – x2
2. (3xy + 4)(4xy – 5) =
4. (y + 2)2 =
12x2y2 – 15xy + 16xy – 20
(y + 2)(y + 2) =
12x2y2 + xy – 20
y2 + 2y + 2y +4 =
y2 + 4y + 4
FHS
Polynomials
6