Chapter 5 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Multiplying Polynomials Multiply a monomial and a polynomial. Multiply two polynomials. Multiply binomials by the FOIL method.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Multiply a monomial and a polynomial. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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 Slide Do not confuse addition of terms with multiplication of terms. For instance,, but

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 1 Multiplying Monomials and Polynomials Solution: Slide Find the product.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Multiply two polynomials. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Multiply two polynomials. We can use the distributive property repeatedly to find the product of any two polynomials. For example, to find the product of the polynomials x 2 + 3x +5 and x − 4, think of x − 4 as a single quantity and use the distributive property as follows. Slide Now use the distributive property three more times to find x 2 (x − 4), 3x(x − 4), and 5(x − 4). This example suggests the following rule. To multiply polynomials, multiply each term of the second polynomial by each term of the first polynomial and add the products.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 2 Multiplying Two Polynomials Slide Multiply (m 3 − 2m + 1)·(2m 2 + 4m + 3). Solution:

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 3 Multiplying Polynomials Vertically Slide Multiply. Solution:

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4 Multiplying Polynomials with Fractional Coefficients Vertically Slide Multiply. Solution:

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4A Multiplying Polynomials with a Rectangle Model Slide Use the rectangle method to find the product Solution:

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3 Objective 3 Multiply binomials by the FOIL method. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Multiply binomials by the FOIL method. Slide 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. A summary of the steps in the FOIL method follows. 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.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 5 Using the FOIL Method Slide Find the product by the FOIL method. Solution:

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 6 Using the FOIL Method Slide Multiply Solution:

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 7 Using the FOIL Method Slide Find each product. Solution: