Warm Up Multiply. Write each product as one power. 1. x · x 2. 62 · 63 3. k2 · k8 4. 195 · 192 5. m · m5 6. 266 · 265 7. Find the volume of a rectangular prism that measures 5 cm by 2 cm by 6 cm. x2 65 k10 197 m6 2611 60 cm3

Learn to multiply polynomials by monomials.

Example 1: Multiplying Monomials A. (2x3y2)(6x5y3) (2x3y2)(6x5y3) Multiply coefficients and add exponents. 12x8y5 B. (9a5b7)(–2a4b3) (9a5b7)(–2a4b3) Multiply coefficients and add exponents. –18a9b10

–21x6y7 Example 2 Multiply. A. (5r4s3)(3r3s2) (5r4s3)(3r3s2) Multiply coefficients and add exponents. 15r7s5 B. (7x3y5)(–3x3y2) (7x3y5)(–3x3y2) Multiply coefficients and add exponents. –21x6y7

To multiply a polynomial by a monomial, use the Distributive Property To multiply a polynomial by a monomial, use the Distributive Property. Multiply every term of the polynomial by the monomial.

Example 3: Multiplying a Polynomial by a Monomial A. 3m(5m2 + 2m) 3m(5m2 + 2m) Multiply each term in parentheses by 3m. 15m3 + 6m2 B. –6x2y3(5xy4 + 3x4) –6x2y3(5xy4 + 3x4) Multiply each term in parentheses by –6x2y3. –30x3y7 – 18x6y3

Example 3: Multiplying a Polynomial by a Monomial C. –5y3(y2 + 6y – 8) –5y3(y2 + 6y – 8) Multiply each term in parentheses by –5y3. –5y5 – 30y4 + 40y3

–3a3b2(4ab3 + 4a2) –12a4b5 – 12a5b2 Example 4 Multiply. A. 4r(8r3 + 16r) 4r(8r3 + 16r) Multiply each term in parentheses by 4r. 32r4 + 64r2 B. –3a3b2(4ab3 + 4a2) –3a3b2(4ab3 + 4a2) Multiply each term in parentheses by –3a3b2. –12a4b5 – 12a5b2

–2x4(x3 + 4x + 3) –2x7 – 8x5 – 6x4 Example 4 Multiply. C. –2x4(x3 + 4x + 3) –2x4(x3 + 4x + 3) Multiply each term in parentheses by –2x4. –2x7 – 8x5 – 6x4

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Multiply. 1. (3a2b)(2ab2) 2. (4x2y2z)(–5xy3z2) 3. 3n(2n3 – 3n) 4. –5p2(3q – 6p) 5. –2xy(2x2 + 2y2 – 2) 6. The width of a garden is 5 feet less than 2 times its length. Find the garden’s length and width if its area is 63 ft2. 6a3b3 –20x3y5z3 6n4 – 9n2 –15p2q + 30p3 –4x3y – 4xy3 + 4xy l = 7 ft, w = 9 ft

Lesson Quiz for Student Response Systems 1. Multiply. (11p2q)(3pq2) A. 14p2q2 B. 14p3q3 C. 33p2q2 D. 33p3q3

Lesson Quiz for Student Response Systems 2. Multiply. 5u(4u3 – 6u) A. 9u4 – 11u2 B. 9u3 – 11u C. 20u4 – 30u2 D. 20u3 – 30u

Lesson Quiz for Student Response Systems 3. Multiply. –8x2(2y – 3x) A. –16x2y + 24x3 B. –6xy – 11x2 C. –16xy + 24x2 D. –16x2y – 11x3 14

Lesson Quiz for Student Response Systems 4. The length of a door is 12 inches less than twice the width. Identify the length and width of the door if its area is 4032 in2. A. l = 84 in. and w = 48 in. B. l = 96 in. and w = 42 in. C. l = 84 in. and w = 42 in. D. l = 96 in. and w = 48 in. 15