1. Warm Up
Multiply. Write each product as one power.
1. x · x
2. 62 · 63
3. k2 · k8
· 192
5. m · m5
· 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

2. Learn to multiply polynomials by monomials.

3. 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

4. –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

5. 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.

6. 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

7. 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

8. –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

9. –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

10. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

11. 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

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

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

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

15. 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