Multiplying Polynomials by Monomials14-5

Warm UpMultiply. Write each product as one power.

1. x · x2. 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

Multiplying Polynomials by Monomials14-5

Learn to multiply polynomials by monomials.

Multiplying Polynomials by Monomials14-5

Multiply.

Example 1: Multiplying Monomials

A. (2x3y2)(6x5y3)

(2x3y2)(6x5y3)

12x8y5

Multiply coefficients and addexponents.

B. (9a5b7)(–2a4b3)

(9a5b7)(–2a4b3)

–18a9b10

Multiply coefficients and addexponents.

Multiplying Polynomials by Monomials14-5

Example 2

Multiply.

A. (5r4s3)(3r3s2)

(5r4s3)(3r3s2)

15r7s5

Multiply coefficients and addexponents.

B. (7x3y5)(–3x3y2)

(7x3y5)(–3x3y2)

–21x6y7

Multiply coefficients and addexponents.

Multiplying Polynomials by Monomials14-5

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

Multiplying Polynomials by Monomials14-5

Multiply.

Example 3: Multiplying a Polynomial by a Monomial

A. 3m(5m2 + 2m)

3m(5m2 + 2m)

15m3 + 6m2

Multiply each term in parentheses by 3m.

B. –6x2y3(5xy4 + 3x4)

–6x2y3(5xy4 + 3x4)

–30x3y7 – 18x6y3

Multiply each term in parentheses by –6x2y3.

Multiplying Polynomials by Monomials14-5

Multiply.

Example 3: Multiplying a Polynomial by a Monomial

C. –5y3(y2 + 6y – 8)

–5y3(y2 + 6y – 8)

–5y5 – 30y4 + 40y3

Multiply each term in parentheses by –5y3.

Multiplying Polynomials by Monomials14-5

Example 4

Multiply.A. 4r(8r3 + 16r)

4r(8r3 + 16r)

32r4 + 64r2

Multiply each term in parentheses by 4r.

B. –3a3b2(4ab3 + 4a2)

–3a3b2(4ab3 + 4a2)

–12a4b5 – 12a5b2

Multiply each term in parentheses by –3a3b2.

Multiplying Polynomials by Monomials14-5

Example 4

Multiply.

C. –2x4(x3 + 4x + 3)

–2x4(x3 + 4x + 3)

–2x7 – 8x5 – 6x4

Multiply each term in parentheses by –2x4.

Multiplying Polynomials by Monomials14-5

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Multiplying Polynomials by Monomials14-5

Lesson QuizMultiply.

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.

–20x3y5z3

6a3b3

6n4 – 9n2

–15p2q + 30p3

l = 7 ft, w = 9 ft

–4x3y – 4xy3 + 4xy

Multiplying Polynomials by Monomials14-5

1. Multiply.(11p2q)(3pq2)

A. 14p2q2

B. 14p3q3

C. 33p2q2

D. 33p3q3

Lesson Quiz for Student Response Systems

Multiplying Polynomials by Monomials14-5

2. Multiply.5u(4u3 – 6u)

A. 9u4 – 11u2

B. 9u3 – 11u

C. 20u4 – 30u2

D. 20u3 – 30u

Lesson Quiz for Student Response Systems

Multiplying Polynomials by Monomials14-5

3. Multiply.–8x2(2y – 3x)

A. –16x2y + 24x3

B. –6xy – 11x2

C. –16xy + 24x2

D. –16x2y – 11x3

Lesson Quiz for Student Response Systems

Multiplying Polynomials by Monomials14-5

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.

Lesson Quiz for Student Response Systems