6 2 Multiplying Polynomials Objectives Multiply polynomials Use
6 -2 Multiplying Polynomials Objectives Multiply polynomials. Use binomial expansion to expand binomial expressions that are raised to positive integer powers. To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents. Holt Algebra 2
6 -2 Multiplying Polynomials Example 1: Multiplying a Monomial and a Polynomial Find each product. A. 4 y 2(y 2 + 3) 4 y 2 + 4 y 2 3 4 y 4 + 12 y 2 B. fg(f 4 + 2 f 3 g – 3 f 2 g 2 + fg 3) fg f 4 + fg 2 f 3 g – fg 3 f 2 g 2 + fg 3 f 5 g + 2 f 4 g 2 – 3 f 3 g 3 + f 2 g 4 Holt Algebra 2
6 -2 Multiplying Polynomials Check It Out! Example 1 Find each product. a. 3 cd 2(4 c 2 d – 6 cd + 14 cd 2) b. x 2 y(6 y 3 + y 2 – 28 y + 30) Holt Algebra 2
6 -2 Multiplying Polynomials To multiply any two polynomials, use the Distributive Property and multiply each term in the second polynomial by each term in the first. Keep in mind that if one polynomial has m terms and the other has n terms, then the product has mn terms before it is simplified. Holt Algebra 2
6 -2 Multiplying Polynomials Example 2 A: Multiplying Polynomials Find the product. (a – 3)(2 – 5 a + a 2) Method 1 Multiply horizontally. (a – 3)(a 2 – 5 a + 2) a(a 2) + a(– 5 a) + a(2) – 3(a 2) – 3(– 5 a) – 3(2) a 3 – 5 a 2 + 2 a – 3 a 2 + 15 a – 6 a 3 – 8 a 2 + 17 a – 6 Holt Algebra 2
6 -2 Multiplying Polynomials Example 2 A: Multiplying Polynomials Find the product. (a – 3)(2 – 5 a + a 2) Method 2 Multiply vertically. a 2 – 5 a + 2 a– 3 – 3 a 2 + 15 a – 6 a 3 – 5 a 2 + 2 a a 3 – 8 a 2 + 17 a – 6 Holt Algebra 2
6 -2 Multiplying Polynomials Check It Out! Example 2 a Find the product. (3 b – 2 c)(3 b 2 – bc – 2 c 2) Holt Algebra 2 Multiply horizontally.
6 -2 Multiplying Polynomials Check It Out! Example 2 b Find the product. Multiply vertically (x 2 – 4 x + 1)(x 2 + 5 x – 2) Holt Algebra 2
6 -2 Multiplying Polynomials Find the product. Holt Algebra 2 (a + 2 b)3
6 -2 Multiplying Polynomials Find the product. Holt Algebra 2 (x + 4)4
6 -2 Multiplying Polynomials Find the product. Holt Algebra 2 (2 x – 1)3
6 -2 Multiplying Polynomials Lesson Quiz Find each product. 1. 5 jk(k – 2 j) 5 jk 2 – 10 j 2 k 2. (2 a 3 – a + 3)(a 2 + 3 a – 5) 2 a 5 + 6 a 4 – 11 a 3 + 14 a – 15 3. (3 a – b)3 Holt Algebra 2 27 a 3 – 27 a 2 b + 9 ab 2 – b 3
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