Page 96 - Math Course 2 (Book 1)

Multiplying Polynomials

Mo. 3

Lesson 7

KEY CONCEPTS: Real World Example
1. Multiply a polynomial by a monomial.
The length of a dog run is 4 feet more than three
times its width. The perimeter of the dog run is 56
feet. What are the dimensions of the dog run?
MO. 3 - L7a
A. 8 ft by 20 ft
Polynomials:
B. 10 ft by 12 ft
Multiplication by Monomial
C. 3 ft by 56 ft

D. 6 ft by 22 ft
Let’s Begin
Explore
You know the perimeter of the dog run. You want to
Product of a Monomial and a f nd the dimensions of the dog run.
Polynomial Plan
Let w represent the width of the dog run.
Examples Then 3w + 4 represents the length.
Write an equation.

Find –8(3x + 2). Perimeter equals twice the sum of the
length and width.
–8(3x + 2) = –8(3x) + (–8)(2) Distributive
Property P = 2 ℓ + w

= –24x – 16 Simplify. Solve
P = 2(ℓ + w) Write the equation.

Answer –24x – 16 56 = 2(3w + 4 + w) Replace P with 56 and ℓ
with 3w + 4.

Find (6x – 1)(–2x). 56 = 2(4w + 4) Combine like terms.

(6x – 1)(–2x) = (6x)(–2x) – 1(–2x) Distributive 56 = 8w + 8 Distributive Property.
Property.
48 = 8w Subtract 8 from each side.

= –12x² + 2x Simplify. 6 = w Divide each side by 8.

D – the width of the dog run is 6
2
Answer –12x + 2x
Answer feet, and the length is 3w + 4 or
22 feet.
2
2
Find 4b(–a + 5ab + 2b ).
Examine
2
2
4b(–a + 5ab + 2b ) P = 2(ℓ + w)

2
2
= 4b(–a ) + 4b(5ab) + 4b(2b ) Distributive = 2(22 + 6)
Property.
= 2(28)
2
3
2
Answer –4a b + 20ab + 8b = 56 The answer checks.
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