Copyright © 2011 Pearson Education, Inc.

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Multiplying Polynomials

Multiply terms.Multiply any two polynomials.Multiply binomials.Find the product of the sum and difference of two terms.Find the square of a binomial.Multiply polynomial functions.

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Slide 5.4- 2Copyright © 2011 Pearson Education, Inc.

Objective 1

Multiply terms.

Find the product.

8k3y(9ky)

EXAMPLE 1

Slide 5.4- 3Copyright © 2011 Pearson Education, Inc.

Objective 2

Multiply any two polynomials.

EXAMPLE 2Find each product.

a. –2r(9r – 5)

b. (2k – 5m)(3k + 2m)

Slide 5.4- 4Copyright © 2011 Pearson Education, Inc.

EXAMPLE 3 Find each product.

a. (4x – 3y)(3x – y)4x – 3y3x – y

Multiply –y(4x – 3y)Multiply 3x(4x – 3y)Combine like terms.

b. (5a3 – 6a2 + 2a – 3)(2a – 5)

Slide 5.4- 5Copyright © 2011 Pearson Education, Inc.

When working with polynomials, the products of two binomials occurs repeatedly. There is a shortcut method for finding these products. First Terms Outer Terms Inner Terms Last terms

CAUTION The FOIL method is an extension of the distributive property, and the acronym “FOIL” applies only to multiplying two binomials.

Objective 3 Multiply binomials.

Slide 5.4- 6Copyright © 2011 Pearson Education, Inc.

EXAMPLE 4Use the FOIL method to find each product.a. (5r – 3)(2r – 5)

b. (4y – z)(2y + 3z)

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Slide 5.4- 7Copyright © 2011 Pearson Education, Inc.

Product of the Sum and Difference of Two TermsThe product of the sum and difference of the two terms x and y is the difference of the squares of the terms. (x + y)(x – y) = x2 – y2

Find the product of the sum and difference of two terms.

Objective 4

Slide 5.4- 8Copyright © 2011 Pearson Education, Inc.

EXAMPLE 5

Find each product.

a. (m + 5)(m – 5)

b. (x – 4y)(x + 4y)

c. 4y2(y + 7)(y – 7)

Slide 5.4- 9Copyright © 2011 Pearson Education, Inc.

Square of a BinomialThe square of a binomial is the sum of the square of the first term, twice the product of the two terms, and the square of the last term. (x + y)2 = x2 + 2xy + y2

(x – y)2 = x2 – 2xy + y2

Objective 5

Find the square of a binomial.

Slide 5.4- 10Copyright © 2011 Pearson Education, Inc.

EXAMPLE 6

Find each product.

a. (t + 9)2

b. (2m + 5)2

c. (3k – 2n)2

Slide 5.4- 11Copyright © 2011 Pearson Education, Inc.

EXAMPLE 7

Find each product.

a. [(x – y) + z][(x – y) – z]

b. (p + 2q)3

Slide 5.4- 12Copyright © 2011 Pearson Education, Inc.

EXAMPLE 7

c. (x + 2)4

Homework: page 270 – 271: # 6-39 every third, 48 – 63 every third