7 7 Multiplying Polynomials Objective Multiply polynomials Holt

7 -7 Multiplying Polynomials Objective Multiply polynomials. Holt Algebra 1

7 -7 Multiplying Polynomials Example 1: Multiplying Monomials Multiply. A. (6 y 3)(3 y 5) (6 3)(y 3 y 5) Group factors with like bases together. 18 y 8 Multiply. B. (3 mn 2) (9 m 2 n) (3 mn 2)(9 m 2 n) (3 9)(m m 2)(n 2 n) 27 m 3 n 3 Holt Algebra 1 Group factors with like bases together. Multiply.

7 -7 Multiplying Polynomials Example 1 C: Multiplying Monomials Multiply. æ 1 2 2ö 2 s t t 12 t s ( ) s ç ÷ 4 è ø ( æ 1 ö 2 g g 12 ÷ s s s ç g ø è 4 ( Holt Algebra 1 ) )(t 2 Group factors with like bases together. gt gt 2 ) Multiply.

7 -7 Multiplying Polynomials Check It Out! Example 1 Multiply. a. (3 x 3)(6 x 2) (3 6)(x 3 x 2) 18 x 5 b. (2 r 2 t)(5 t 3) Holt Algebra 1 Group factors with like bases together. Multiply. (2 r 2 t)(5 t 3) Group factors with like bases together. (2 5)(r 2)(t 3 t) 10 r 2 t 4 Multiply.

7 -7 Multiplying Polynomials Check It Out! Example 1 Multiply. æ 1 2 ö 3 2 4 5 x y 12 x z )( y z c. ç ÷( è 3 ø ) æ 1 2 ö 3 2 x y 12 x z ÷ ç ø è 3 )(y z ) æ 1 g ö 2 g 3 12÷ x x ç ø è 3 )(y gy )(z ( ( 4 x 5 y 5 z 7 Holt Algebra 1 4 5 4 Group factors with like bases together. 2 ) gz 5 Multiply.

7 -7 Multiplying Polynomials Example 2 A: Multiplying a Polynomial by a Monomial Multiply. 4(3 x 2 + 4 x – 8) Distribute 4. (4)3 x 2 +(4)4 x – (4)8 Multiply. 12 x 2 + 16 x – 32 Holt Algebra 1

7 -7 Multiplying Polynomials Check It Out! Example 2 Multiply. a. 2 x(4 x 2 + x + 3) 2(4 x 2 + x + 3) Distribute 2. 2(4 x 2) + 2(x) + 2(3) Multiply. 8 x 2 + 2 x + 6 Holt Algebra 1

7 -7 Multiplying Polynomials Check It Out! Example 2 Multiply. b. 3 ab(5 a 2 + b) Distribute 3 ab. (3 ab)(5 a 2) + (3 ab)(b) (3 5)(a a 2)(b) + (3)(a)(b b) 15 a 3 b + 3 ab 2 Holt Algebra 1 Group like bases together. Multiply.

7 -7 Multiplying Polynomials Check It Out! Example 2 Multiply. c. 5 r 2 s 2(r – 3 s) Distribute 5 r 2 s 2. (5 r 2 s 2)(r) – (5 r 2 s 2)(3 s) (5)(r 2 r)(s 2) – (5 3)(r 2)(s 2 s) 5 r 3 s 2 – 15 r 2 s 3 Holt Algebra 1 Group like bases together. Multiply.

7 -7 Multiplying Polynomials To multiply a binomial by a binomial, you can apply the Distributive Property more than once: (x + 3)(x + 2) = x(x + 2) + 3(x + 2) Distribute x and 3 again. = x(x) + x(2) + 3(x) + 3(2) Multiply. = x 2 + 2 x + 3 x + 6 Combine like terms. = x 2 + 5 x + 6 Holt Algebra 1

7 -7 Multiplying Polynomials Example 3 A: Multiplying Binomials Multiply. (s + 4)(s – 2) s(s – 2) + 4(s – 2) Distribute s and 4. s(s) + s(– 2) + 4(s) + 4(– 2) s 2 – 2 s + 4 s – 8 Distribute s and 4 again. Multiply. s 2 + 2 s – 8 Combine like terms. Holt Algebra 1

7 -7 Multiplying Polynomials Example 3 C: Multiplying Binomials Multiply. (8 m 2 – n)(m 2 – 3 n) Use the FOIL method. 8 m 2(m 2) + 8 m 2(– 3 n) – n(m 2) – n(– 3 n) 8 m 4 – 24 m 2 n – m 2 n + 3 n 2 Multiply. 8 m 4 – 25 m 2 n + 3 n 2 Combine like terms. Holt Algebra 1

7 -7 Multiplying Polynomials Check It Out! Example 3 c Multiply. (2 a – b 2)(a + 4 b 2) Use the FOIL method. 2 a(a) + 2 a(4 b 2) – b 2(a) + (–b 2)(4 b 2) 2 a 2 + 8 ab 2 – 4 b 4 Multiply. 2 a 2 + 7 ab 2 – 4 b 4 Combine like terms. Holt Algebra 1