Intermediate Algebra (11th edition)

SECTION 5.4 Multiplying Polynomials 293

OBJECTIVES

Multiplying Polynomials

5.4

1 Multiply terms.

2 Multiply any two

polynomials.

3 Multiply binomials.

4 Find the product

of the sum and

difference of

two terms.

5 Find the square of

a binomial.

6 Multiply polynomial

functions.

Multiplying Monomials

Find each product.

(a)

Commutative and associative properties

Multiply; product rule for exponents

Add the exponents.

(b)

=- 12 a^8

=- 4132 a^3 #a^5

- 4 a^3 13 a^52

= 15 x^7

= 15 x^4 +^3

= 3 # 5 #x^4 #x^3

13 x^4215 x^32

EXAMPLE 1

(c)

= 16 m^5 z^6 NOW TRY

= 2182 m^2 #m^3 #z^4 #z^2

2 m^2 z^418 m^3 z^22

Multiplying Polynomials

Find each product.

(a)

Distributive property

Multiply.

(b)

Distributive property

Multiply.

(c)

Distributive property;

Multiply each term of

by

Multiply.

Combine like terms.

(d)

Distributive property

Distributive property

Combine like terms.

= 2 x^4 - 4 x^3 - 6 x 2 Distributive property NOW TRY

= 2 x^21 x^2 - 2 x- 32

= 2 x^23 x^2 +x- 3 x- 34

= 2 x^231 x+ 121 x 2 + 1 x+ 121 - 324

2 x^21 x+ 121 x- 32

= 6 x^3 - 5 x^2 - 4 x

= 6 x^3 - 8 x^2 + 3 x^2 - 4 x

= 3 x 12 x^22 + 1 - 4212 x^22 + 13 x 21 x 2 + 1 - 421 x 2

= 13 x- 4212 x^22 + 13 x- 421 x 2

2 x^2 +x 3 x-4.

13 x- 4212 x^2 +x 2

13 x- 4212 x^2 +x 2

=- 20 x^4 + 15 x^3 - 10 x^2

= 5 x^21 - 4 x^22 + 5 x^213 x 2 + 5 x^21 - 22

5 x^21 - 4 x^2 + 3 x- 22

=- 16 x 3 + 18 x^2

= - 218 x^32 - 21 - 9 x^22

- 218 x^3 - 9 x^22

EXAMPLE 2

Treat 3x 4 ⎧⎪⎨⎪⎩

as a single

expression.

• 
  

NOW TRY
EXERCISE 1
Find the product.

• 3 s^2 t 115 s^3 t^42

NOW TRY ANSWERS

1. 
   

2. (a)
   (b) 10 x^3 + 35 x^2 - 20 x
   
   
   • 6 k^8 + 9 k^5 - 12 k^3
   
   
   
   

• 45 s^5 t^5

NOW TRY
EXERCISE 2
Find each product.

(a)

(b) 5 x 12 x- 121 x+ 42

3 k^31 - 2 k^5 + 3 k^2 - 42

OBJECTIVE 2 Multiply any two polynomials.

OBJECTIVE 1 Multiply terms.

Distributive property

Be careful with signs.