# The Distributive Property by yurtgc548

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```									The Distributive
Property
Algebra; Section 2.6
Goal 1:
Using the Distributive Property
¢   Rules
l The Distributive Property
Example 1:
Using an Area Model
¢       Find the area of a rectangle whose
width is 3 and whose length is x + 2.
¢       Solution
l Draw a picture:

3                    3     3x       6

x+2               x       2
Example 1:
Using an Area Model
¢       Solution
l Draw a picture:

3                   3   3x      6

x+2             x      2
l The picture would lead us to believe
that the area is 3x + 6.
The Distributive Property

¢   a(b + c) = ab + ac.
¢   a(b – c) = ab – ac.
¢   The factor on the outside gets
distributed to both of the terms on
the inside.
Example 2:
Using the Distributive Property
¢   Find the following products:
l   2(x + 5)
l   (x – 4)x
l   (1 + 2x)8
l   y(1 – y)
Example 2:
Using the Distributive Property
¢   Solution:
l   2(x + 5) = 2x + 2(5) = 2x + 10
l   (x – 4)x = x2 – 4x
l   (1 + 2x)8 = 8(1) + 8(2x) = 8 + 16x
l   y(1 – y) = 1y – y2 = y – y2
Example 3:
Using the Distributive Property
¢   Find the following products:
l   -3(x + 4)
l   (y + 5)(-4)
l   -(6 – 3x)
l   (x – 1)(-9x)
Example 3:
Using the Distributive Property
¢   Solution:
l   -3(x + 4) = -3x + (-3)(4) = -3x – 12
l   (y + 5)(-4) = -4y + (-4)(5) = -4y – 20
l   -(6 – 3x) = -6 – -(3x) = -6 + 3x
l   (x – 1)(-9x) = -9x2 – 1(-9x) =
-9x2 + 9x
Example 4:
Mental Math Calculations
¢   You are shopping for CDs. You
want to buy 6 CDs for \$11.95 each.
Use the Distributive Property to
calculate the total cost.
¢   Solution
l Think of \$11.95 as \$12.00 – \$.05.
l 6(12 – .05) = 6(12) – 6(.05)
l 6(12) – 6(.05) = 72.00 – .30 =
\$71.70
Extra Example:
Mental Math Calculations
¢   Find the following products:
l 29(30)
l 41(11)
¢   Solution
l 29(30) = (30 – 1)(30) =
900 – 30 = 870
l 41(11) = 41(10 + 1) =
410 + 41 = 451
In-Class Assignment

¢   Do #3-12 on page 103.
Goal 2:
Simplifying by Combining Like Terms

¢   Vocabulary
l   Coefficient
l   Like terms
l   Constant terms
l   Simplified
Example 5:
Simplifying by Combining Like Terms

¢    Simplify the following:
l 8x + 3x
l 4x2 + 2 – x2
l 3 – 2(4 + x)
¢    Solution
l 8x + 3x = (8 + 3)x = 11x
l 4x2 + 2 – x2 = (4 – 1)x2 + 2 = 3x2 + 2
l 3 – 2(4 + x) = 3 – 2(4) – 2(x) =
3 – 8 – 2x = -5 – 2x
Example 6:
Using the Distributive Property to
Simplify a Function
¢   It takes you 45 minutes to get to
school. You spend t minutes
walking to the bus stop, and then the
rest of the time riding the bus. You
walk .06 miles/minute and the bus
travels .5 miles/minutes. The total
distance you travel is given by the
function D = .06t + .5(45 – t).
Simplify this function.
Example 6:
Using the Distributive Property to
Simplify a Function
¢    Solution:
l D = .06t + .5(45 – t) =
.06t + .5(45) + .5(-t)
l .06t + .5(45) + .5(-t) =
.06t + 22.5 – .5t
l .06t + 22.5 – .5t = -.44t + 22.5
In-Class Assignment

¢   Do #1,2, and #13-18 on page 103.
Assignment

¢   Do #19-24 all, #26-68 evens, and
#70-78 all on pages 103-104.

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