YOU TRY 1 Multiply. Count how many times the distributive property is used. EXAMPLE 2 In-Class Example 2 Multiply. a) (k 3)(k 4) b) (c2 4)(3c3 c 8) Answer: a) k2 k 12 b) 3c5 13c3 8c2 4c 32 Write out each example as you are reading it. a) 3c2(9c 2) b) 4a4(a2 5a 3) 2 Multiply Two Polynomials To multiply two polynomials, we use the distributive property repeatedly. For example, to multiply (2x 3)(x2 7x 4), we multiply each term in the second polynomial by (2x 3). (2x 3)(x2 7x 4) (2x 3)(x2) (2x 3)(7x) (2x 3)(4) Distribute. Next, we distribute again. (2x 3)(x2) (2x 3)(7x) (2x 3)(4) (2x)(x2) (3)(x2) (2x)(7x) (3)(7x) (2x)(4) (3)(4) 2x3 3x2 14x2 21x 8x 12 Multiply. 2x3 17x2 29x 12 Combine like terms. This process of repeated distribution leads us to the following rule. Procedure Multiplying Polynomials To multiply two polynomials, multiply each term in the second polynomial by each term in the fi rst polynomial. Then combine like terms. The answer should be written in descending powers. Let’s use this rule to multiply the polynomials in Example 2. Multiply. a) (x 2)(x 7) b) (n2 5)(2n3 n 9) Solution a) Multiply each term in the second polynomial by each term in the fi rst polynomial. (x 2)(x 7) x(x) x(7) 2(x) 2(7) x2 (7x) 2x (14) x2 5x 14 Combine like terms. b) Multiply each term in the second polynomial by each term in the fi rst. (n2 5)(2n3 n 9) (n2)(2n3) (n2)(n) (n2)(9) (5)(2n3) (5)(n) (5)(9) Distribute. 2n5 n3 9n2 10n3 5n 45 Multiply. 2n5 11n3 9n2 5n 45 Combine like terms. YOU TRY 2 Multiply. a) (y 8)(y 3) b) (w2 6)(5w3 w2 4w) 798 CHAPTER 10 The Rules of Exponents and Polynomials www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
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