Download The Distributive Property

1.4
The Distributive Property
Goal
O Use the distributive property to evaluate and
simplify expressions.
Distributive Property
For any numbers a, b, and c,
a(b + c) = ab + ac
a(b – c)= ab – ac
Example: 3(2 + 5) = 3∙2 + 3∙5
3 (7) = 6 + 15
21 = 21
The symmetric property
allows…
The distributive property to be written as
follows:
If a(b + c) = ab + bc, then ab + bc = a(b + c)
Ex. 1
O A group of 7 adults and 6 children are going
to a University of South Florida Bulls
baseball game. Use the distributive Property
to write and evaluate an expression for the
total ticket cost.
USF Bulls Baseball Tickets
Ticket
Cost
Adult Single Game
5
Children single game (12 and
under)
3
Groups of 10 or more single game 2
Senior single game (65+)
3
Ex. 2
Julio walks 5 days a week. He walks at a fast
rate for 7 minutes and cools down for 2
minutes. Use the Distributive Property to write
and evaluate an expression that determines
the total number of minutes Julio walks.
Ex. 4- making mental math
easier
O Use the distributive property to rewrite 7 ∙ 49
Ex. 3
Use the distributive property to rewrite 12 ∙ 82
Practice
1. 304(15)
Ex. 6
O Rewrite each expression using the
Distributive Property. Then simplify
7(3w – 5)
Practice
1. (6𝑣 2 + 𝑣 − 3)4
Practice
O 2. −6 𝑟 + 3𝑔 − 𝑡
O 3.
2 − 5𝑞 −3
O 4. 4(𝑦 2 + 8𝑦 + 2)
Like Terms
O Terms that contain the same variables, with
corresponding variables having the same
power.
O Ex: 6𝑎2 + 𝑎2 + 2𝑎
Think about this..
O The distributive property and the properties
of equality can be used to show that
4k+8k=12k.
O 4k + 8k= (4+8)k
= 12k
Combine Like Terms
Ex. 7a)
Simplify
Ex. 7b) Simplify
17u + 25u
6𝑡 2 + 3𝑡 − 𝑡
Ex. 8
Simplify 12𝑏 2 − 8𝑏 2 + 6𝑏
Practice 1. 4𝑦 3 + 2𝑦 − 8𝑦 + 5
Ex. 9
O Use the expression twice the difference of
3x and y increased by five times the sum of
x and 2y.
1. Write an algebraic expression for the verbal
expression.
2. Simplify the expression and indicated the
properties used.
Coefficient
O The coefficient of a term is the numerical
factor.
O Examples: State the coefficients
6ab
𝑥2
3
y
Pg. 30 38,49-52,76