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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