13 5 Multiplying Polynomials by Monomials Remember that

13 -5 Multiplying Polynomials by Monomials Remember that when you multiply two powers with the same bases, you add the exponents. To multiply two monomials, multiply the coefficients and add the exponents of the 2 3 3 6 (5 m n )(6 m n ) variables that are the same. 5 · 6 · m 2+3 n 3+6 30 m 5 n 9 Pre-Algebra

13 -5 Multiplying Polynomials by Monomials Multiplying Monomials Multiply. A. (2 x 3 y 2)(6 x 5 y 3) 12 x 8 y 5 Multiply coefficients and add exponents. B. (9 a 5 b 7)(– 2 a 4 b 3) – 18 a 9 b 10 Pre-Algebra Multiply coefficients and add exponents.

13 -5 Multiplying Polynomials by Monomials Insert Lesson Title Here Try This Multiply. A. (5 r 4 s 3)(3 r 3 s 2) 15 r 7 s 5 Multiply coefficients and add exponents. B. (7 x 3 y 5)(– 3 x 3 y 2) – 21 x 6 y 7 Pre-Algebra Multiply coefficients and add exponents.

13 -5 Multiplying Polynomials by Monomials To multiply a polynomial by a monomial, use the Distributive Property. Multiply every term of the polynomial by the monomial. Pre-Algebra

13 -5 Multiplying Polynomials by Monomials Multiplying a Polynomial by a Monomial Multiply. A. 3 m(5 m 2 + 2 m) 15 m 3 + 6 m 2 Multiply each term in parentheses by 3 m. B. – 6 x 2 y 3(5 xy 4 + 3 x 4) – 30 x 3 y 7 – 18 x 6 y 3 Pre-Algebra Multiply each term in parentheses by – 6 x 2 y 3.

13 -5 Multiplying Polynomials by Monomials Multiplying a Polynomial by a Monomial Multiply. C. – 5 y 3(y 2 + 6 y – 8) – 5 y 5 – 30 y 4 + 40 y 3 Pre-Algebra Multiply each term in parentheses by – 5 y 3.

13 -5 Multiplying Polynomials by Monomials Insert Lesson Title Here Try This: Example 2 A & 2 B Multiply. A. 4 r(8 r 3 + 16 r) 32 r 4 + 64 r 2 Multiply each term in parentheses by 4 r. B. – 3 a 3 b 2(4 ab 3 + 4 a 2) – 12 a 4 b 5 – 12 a 5 b 2 Pre-Algebra Multiply each term in parentheses by – 3 a 3 b 2.

13 -5 Multiplying Polynomials by Monomials Insert Lesson Title Here Example 2 Multiply. C. – 2 x 4(x 3 + 4 x + 3) – 2 x 7 – 8 x 5 – 6 x 4 Pre-Algebra Multiply each term in parentheses by – 2 x 4.

13 -5 Multiplying Polynomials by Monomials Insert Lesson Title Here Multiply. Lesson Quiz 1. (3 a 2 b)(2 ab 2) 6 a 3 b 3 2. (4 x 2 y 2 z)(– 5 xy 3 z 2) – 20 x 3 y 5 z 3 3. 3 n(2 n 3 – 3 n) 6 n 4 – 9 n 2 4. – 5 p 2(3 q – 6 p) – 15 p 2 q + 30 p 3 5. – 2 xy(2 x 2 + 2 y 2 – 2) Pre-Algebra – 4 x 3 y – 4 xy 3 + 4 xy