chapter 5 section 5. copyright © 2012, 2008, 2004 pearson education, inc. objectives 1 copyright ©...

Chapter 5 Section 5

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


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.


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 68 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 57 2 9q q q 5 5 5 5 107 2 7 2 14 .q q q q

Slide 5.5-4


Solution:

Find the product.

4 22 3 2 5x x x

424 43 2 52 2 2x x xx x

6 5 46 4 10x 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 24 4 45 5 43 3x x xx x xx x

Now use the distributive property three more times to find x2(x − 4), 3x(x − 4), and 5(x − 4).

Multiplying PolynomialsTo 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 54 4 4x xx x x x x

3 2 24 3 12 5 20x x x x x 3 2 7 20x 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 22 4 3 4 8 6 2 4 3m m m m m m m m 5 4 3 22 4 6 2 3m m m m m

Slide 5.5-8

EXAMPLE 2 Multiplying Two Polynomials


Multiply.

23 4 5x x 4x

212 16 20x x 3 23 4 5x x x

3 23 16 11 20x x x

Solution:

Slide 5.5-9

EXAMPLE 3 Multiplying Polynomials Vertically


Multiply.

3 25 10 20x x 21 2

5 5x

3 22 4 8x x 5 4 3 22 0 4x x x x

5 4 32 2 8x x x

Solution:

Slide 5.5-10

EXAMPLE 4 Multiplying Polynomials with Fractional Coefficients Vertically


Objective 3


Slide 5.5-11



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 MethodStep 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 5x x

2F x L 15

O 5x I 3xSlide 5.5-12


Use the FOIL to find the product.

2 6x x

2 6 2 8x x x 2 8 12x x

Solution:

2F 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 18xy x y

Solution:

5 6 2 3x y

F 10xy L 18

O 15x I 12y

Slide 5.5-14



Find each product.

4 2 3y x y x

2 28 12 2 3y xy xy x Solution:

33 2 2 1x x x

2 28 14 3y xy x

3 23 2 1 4 2x x x x

3 23 2 3 2x x x 5 4 36 9 6x x x

Slide 5.5-15


chapter 5 section 5. copyright © 2012, 2008, 2004 pearson education, inc. objectives 1 copyright ©...

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