Download Lesson 8-7 Multiplying Polynomials

Lesson 7-7
Multiplying Polynomials
p. 447
FOIL



There are two methods that can be
used to multiply polynomials
The first is called FOIL.
FOIL Stands for:




First
Outer
Inner
Last
Example
 x  3 x  2
2
x
x

x
x

3
x

2
  
 

 x  3 x  2  x  2  2x
 x  3 x  2  3 x   3x

Use FOIL to solve
1.
Multiply the First
Terms
Multiply the Outer
Terms
Multiply the Inner
Terms
Multiply the Last
x

3
x

2


 3 2  6
Terms
2
Add the four
x  2 x  3x  6
products and
2
combine Like Terms
x  x6
2.
3.
4.
5.
Use FOIL to solve
 x  5 x  7 
F
O
I
L
 x  x    x  7    5 x    5 7 
x 2 2 7 x  5 x  35
x  2 x  35
 2 y  3 6 y  7 
F
O
I
L
 2 y  6 y    2 y  7    3 6 y    3 7 
12 y 2  14 y  18 y  21
12 y 2  4 y  21
Problems to Try
Simplify by using the FOIL method.
1.  y  8 y  4
2.  z  6 z 12
The Distributive Property



The FOIL Method only works when
you multiply two binomials
The other method used in multiplying
polynomials uses the Distributive
Property
The Distributive Property always
works!
Example

1.
2.
3.
4.



Use the Distributive
x3 x2
Property to Solve
 x  3 x  2
Split the first
polynomial up and
x  x  2  3  x  2
write each term
multiplied by the
second polynomial
x  x   x  2  3  x   3  2
Distribute
2
x
 2 x  3x  6
Multiply
Combine Like Terms
x2  x  6
Use the Distributive Property
to Solve
 x  3 x  2
x  x  2  3  x  2
x  x   x  2  3  x   2 3
x 2  2 x  3x  6
x2  5x  6


2
4
x

9
2
x
 5x  3
FOIL would not work here!


4 x  2 x 2  5 x  3  9  2 x 2  5 x  3
4 x 2 x 2  4 x  5 x   4 x  3  9 2 x 2  9  5 x   9  3 
8 x3  20 x 2  12 x  18 x 2  45 x  27



8 x  2 x  33 x  27
3
2

Multiplying two trinomials



y2  2 y  5 6 y2  3y 1



 

y2 6 y2  3y 1  2 y 6 y2  3y 1  5 6 y2  3y 1






y 2 6 y 2  y 2  3 y   y 2 1  2 y 6 y 2  2 y  3 y   2 y 1  5 6 y 2  5  3 y   5 1
6 y 4  3 y3  y 2  12 y3  6 y 2  2 y  30 y 2  15 y  5
6 y  15 y  37 y  17 y  5
4
3
2
Problems to Try
Simplify using the Distributive Property
1. 5x  4 2 x  8
2
3
a

4
a
 12a  1



2.
3. 


2b 2  7b  9 b 2  3b  1
Word Problem
1.
Translate the equation
2.
Substitute your values
A  12 h  b1  b2 
A
3.
1
2
 x  2   3x  7    2 x  1
Simplify
A  12  x  2 5x  6
A  x  2x  6
A  12  x  5 x    x  6    2  5 x    2  6  
A  12 5 x 2  6 x  10 x  12
A  12  5 x 2  4 x  12 

A
1
2

 
5 x 2  12  4 x   12  12 
5
2
2
Problem to Try
1.
AlgeBlocks
x  7 x  10
2