8-Multiplying Polynomials. Mathematics 8

Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objectives
1
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Multiply a monomial and a polynomial.
Multiply two polynomials.
Multiply binomials by the FOIL method.
5.5
2
3
Copyright © 2012 Pearson Education, Inc.
Multiplying Polynomials

Objective 1
Multiply a monomial and a
polynomial.
Slide 5.5-3

To find the product of a monomial and a polynomial with more than one
term we use the distributive property and multiplication of monomials.
Multiply a monomial and a polynomial.
As shown in Section 5.1, we find the product of two monomials by
using the rules for exponents and the commutative and associative
properties. For example
     
6 6 6 6 6 6
8 9 8 9 72 .
m n m n m n
    
Do not confuse addition of terms with multiplication of terms. For
instance,
but
5 5 5
7 2 9
q q q
    
5 5 5 5 10
7 2 7 2 14 .
q q q q

  
Slide 5.5-4

Solution:
Find the product.
 
4 2
2 3 2 5
x x x
 
     
4
2
4 4
3 2 5
2 2 2
x x x
x x
     
6 5 4
6 4 10
x x x
  
Slide 5.5-5
EXAMPLE 1 Multiplying Monomials and Polynomials

Objective 2
Slide 5.5-6

We can use the distributive property repeatedly to find the product of
any two polynomials. For example, to find the product of the
polynomials x2
+ 3x +5 and x − 4, think of x − 4 as a single quantity
and use the distributive property as follows.
        
2 2
4 4 4
5 5 4
3 3
x x x
x x x
x x
  
    

Now use the distributive property three more times to find x2
(x − 4),
3x(x − 4), and 5(x − 4).
Multiplying Polynomials
To multiply two polynomials, multiply each term of the second
polynomial by each term of the first polynomial and add the products.
           
2 2
3 3 5 5
4 4 4
x x
x x x x x
     
  
     
3 2 2
4 3 12 5 20
x x x x x
        
3 2
7 20
x x x
   
Slide 5.5-7

Multiply (m3
− 2m + 1)·(2m2
+ 4m + 3).
Solution:
           
        
3 2 3 3 2
2
2 4 3 2 2 2 4
2 3 1 2 1 4 1 3
m m m m m m m m m
m m m
      
    
     
5 4 3 3 2 2
2 4 3 4 8 6 2 4 3
m m m m m m m m
           
5 4 3 2
2 4 6 2 3
m m m m m
     
Slide 5.5-8
EXAMPLE 2 Multiplying Two Polynomials

Multiply.
2
3 4 5
x x
 
4
x 
2
12 16 20
x x
 
3 2
3 4 5
x x x
 
3 2
3 16 11 20
x x x
  
Solution:
Slide 5.5-9
EXAMPLE 3 Multiplying Polynomials Vertically

Multiply.
3 2
5 10 20
x x
 
2
1 2
5 5
x 
3 2
2 4 8
x x
 
5 4 3 2
2 0 4
x x x x
  
5 4 3
2 2 8
x x x
  
Solution:
Slide 5.5-10
EXAMPLE 4 Multiplying Polynomials with Fractional Coefficients Vertically

Objective 3
Multiply binomials by the FOIL
method.
Slide 5.5-11

Multiply binomials by the FOIL method.
In algebra, many times the polynomials to be multiplied are
binomials. For these products, the FOIL method reduces the
rectangle method to a systematic approach without the rectangle.
Multiplying Binomials by the FOIL Method
Step 1: Multiply the two First terms of the binomials to get the
first term of the answer.
Step 2: Find the Outer product and Inner product and add them
(when possible) to get the middle term of the answer.
Step 3: Multiply the two Last terms of the binomials to get the
last term of the answer.
  
3 5
x x
 
2
F x
 L 15

O 5x
 I 3x

Slide 5.5-12

Use the FOIL to find the product.
  
2 6
x x
 
2
6 2 8
x x x
   
2
8 12
x x
  
Solution:
2
F x

O 6x
 I 2x

L 12

Slide 5.5-13
EXAMPLE 5 Using the FOIL Method

Multiply   
5 6 2 3 .
x y
 
10 15 12 18
xy x y
   
Solution:
  
5 6 2 3
x y
 
F 10xy
 L 18

O 15x
 I 12y

Slide 5.5-14

Find each product.
  
4 2 3
y x y x
  
2 2
8 12 2 3
y xy xy x
   
Solution:
  
3
3 2 2 1
x x x
 
2 2
8 14 3
y xy x
  
 
3 2
3 2 1 4 2
x x x x
   
 
3 2
3 2 3 2
x x x
  
5 4 3
6 9 6
x x x
  
Slide 5.5-15

8-Multiplying Polynomials. Mathematics 8

More Related Content

Similar to 8-Multiplying Polynomials. Mathematics 8 (20)

More from ChristeusVonSujero1 (20)

Recently uploaded (20)

8-Multiplying Polynomials. Mathematics 8