Transcript Lesson 6-2

Lesson 8-6
Multiplying Polynomials
by a Monomial
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Objectives
• Find the product of a monomial and a
polynomial
• Solve equation involving polynomials
Vocabulary
• none new – sorry no definitions! Check back
tomorrow for some!! ^-^
Multiplying Polynomials
• Use the Distributive Property of Equality!
• Example: 6x(2x2 + 3xy – 5y3 + 4)
= 6x(2x2) + 6x(3xy) – 6x(5y3) + 6x(4)
= 12x3 + 18x2y – 30xy3 + 24x
Example 1
Find 6y(4y2 – 9y – 7)
Method 1 Horizontal
Distributive Property
Multiply.
Method 2 Vertical
Distributive Property
Multiply.
Answer:
Example 2
Simplify 3(2t2 – 4t – 15) + 6t(5t + 2)
Distributive Property
Product of Powers
Commutative and
Associative
Properties
Combine like terms.
Answer:
Example 3
Entertainment Admission to the Super Fun
Amusement Park is $10. Once in the park, super rides
are an additional $3 each and regular rides are an
additional $2. Sarita goes to the park and rides 15
rides, of which s of those 15 are super rides.
Find an expression for how much money Sarita spent
at the park.
Words
The total cost is the sum of the admission,
super ride costs, and regular ride costs.
Variables If
the number of super rides, then
is the number of regular rides. Let M be the
amount of money Sarita spent at the park.
Example 3 cont
Equation
Amount
super
$3 per
regular
$2 per
of money equals admission plus rides times ride plus rides times ride.
M
10
s
3
2
Distributive Property
Simplify
Simplify.
Answer: An expression for the amount of money Sarita
spent in the park is
, where s is the number of super
rides she rode.
Example 3 cont
Evaluate the expression to find the cost if Sarita
rode 9 super rides.
Add.
Answer: Sarita spent $49.
Example 4
Solve b(12 + b) – 7 = 2b + b(-4 + b)
Original equation
Distributive Property
Combine like terms.
Subtract
from each side.
Add 7 to each side.
Add 2b to each side.
Divide each side by 14.
Answer:
Summary & Homework
• Summary:
– The Distributive Property can be used to multiply a
polynomial by a monomial
• Homework:
– pg. 446 16-48 even