7 7 Multiplying Polynomials Objective Multiply two binomials

7 -7 Multiplying Polynomials Objective Multiply two binomials. Holt Algebra 1

7 -7 Multiplying Polynomials Check It Out! Example 1 Multiply. a. (4 x 3)(6 x 7) Group factors with like bases together. (4 x 3)(6 x 7) (4 6)(x 3 x 7) 24 x 10 Multiply. b. (3 rt 4)(5 t 3) Group factors with like bases together. (3 rt 4)(5 t 3) (3 5)(r)(t 4 15 rt 7 Holt Algebra 1 t 3 ) Multiply.

7 -7 Multiplying Polynomials Check It Out! Example 2 Multiply. b. 2 ab(5 a 5 + 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 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 3 + 4 b 2) Use the FOIL method. 2 a(a 3) + 2 a(4 b 2) – b 2(a 3) + (–b 2)(4 b 2) 2 a 4 + 8 ab 2 – a 3 b 2 – 4 b 4 Holt Algebra 1 Multiply.