Multiply polynomials When multiplying powers with the same base, keep the base and add the exponents. x2  x3 = x2+3 = x5 Example 1: Multiplying Monomials.

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Multiply polynomials When multiplying powers with the same base, keep the base and add the exponents. x2  x3 = x2+3 = x5 Example 1: Multiplying Monomials A. (6y3)(3y5) (6y3)(3y5) Group factors with like bases together. (6 ● 3)(y3 ● y5) Group factors with like bases together. Multiply 18y8 Multiply B. (3mn2) (9m2n) (3mn2)(9m2n) Group factors with like bases together. (3 ● 9)(m ● m2)(n2 ● n) Group factors with like bases together. 27m3n3 Multiply

To multiply a polynomial by a monomial, use the Distributive Property. Example 2: Multiplying a Polynomial by a Monomial C. 3ab(5a2 + b) 3ab(5a2 + b) (3ab)(5a2) + (3ab)(b) Distribute 3ab. (3  5)(a  a2)(b) + (3)(a)(b  b) Group like bases together. 15a3b + 3ab2 Multiply Example 3A: Multiplying a Binomial by a Binomial To multiply a binomial by a binomial, you can apply the Distributive Property more than once: D. (x + 3)(x + 2) = x(x + 2) + 3(x + 2) Distribute x and 3. = x(x + 2) + 3(x + 2) Distribute x and 3 again. = x(x) + x(2) + 3(x) + 3(2) Multiply = x2 + 2x + 3x + 6 Combine like terms. = x2 + 5x + 6

1. Multiply the First terms. (x + 3)(x + 2) x x = x2 Example 3B: Multiplying a Binomial by a Binomial Another method for multiplying binomials is called the FOIL method. 1. Multiply the First terms. (x + 3)(x + 2) x x = x2  2. Multiply the Outer terms. (x + 3)(x + 2) x 2 = 2x  3. Multiply the Inner terms. (x + 3)(x + 2) 3 x = 3x  4. Multiply the Last terms. (x + 3)(x + 2) 3 2 = 6  (x + 3)(x + 2) = x2 + 2x + 3x + 6 = x2 + 5x + 6 F O I L

(s + 4)(s – 2) s(s – 2) + 4(s – 2) Distribute s and 4. s(s) + s(–2) + 4(s) + 4(–2) Distribute s and 4 again. s2 – 2s + 4s – 8 Multiply s2 + 2s – 8 Combine like terms.