10.5 Multiplying Polynomials What are your objectives for Section 10.5? How can you accomplish each objective? 1 Multiply a Monomial and a Polynomial • Understand which properties to use to complete this objective. • Complete the given example on your own. • Complete You Try 1. 2 Multiply Two Polynomials • Follow the explanation to fully understand the procedure for Multiplying Polynomials, and write an example in your notes. • Complete the given examples on your own. • Complete You Trys 2 and 3. Read the explanations, follow the examples, take notes, and complete the You Trys. We have already learned that when multiplying two monomials, we multiply the coeffi cients and add the exponents of the same bases: 2n3 5n3 10n6 Don’t confuse the product of terms with the sum of terms. Product Sum 2n3 5n3 12 52n33 10n6 2n3 5n3 12 52n3 7n3 In this section, we will discuss how to multiply other types of polynomials. 1 Multiply a Monomial and a Polynomial To multiply a monomial and a polynomial, we use the distributive property. EXAMPLE 1 In-Class Example 1 Multiply. a) 6x2(4x 7) b) 5p3(9p2 8p 2) Answer: a) 24x3 42x2 b) 45p5 40p4 10p3 Multiply. a) 8k2(2k 3) b) 7y3(6y2 4y 1) Solution a) Use the distributive property. 2(2k 3) (8k 8k 2)(2k) (8k 2)(3) Distribute. 16k3 24k2 Multiply. b) 7y3(6y2 4y 1) (7y3)(6y2) (7y3)(4y) (7y3)(1) Distribute. 42y5 28y4 (7y3) Multiply. 42y5 28y4 7y3 www.mhhe.com/messersmith SECTION 10.5 Multiplying Polynomials 797
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