Notes­10.19 Distributive Property
October 19, 2015
10.19
Grade: «grade»
Subject:«subject»
Date:«date»
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Notes­10.19 Distributive Property
Good Day!
October 19, 2015
19 October 2015
Homework: Think about It Problem due Friday 10.23
Weekly Exercises due Monday 10.26
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Notes­10.19 Distributive Property
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Notes­10.19 Distributive Property
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Problem Solving
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Notes­10.19 Distributive Property
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Notes­10.19 Distributive Property
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Notes­10.19 Distributive Property
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Problem Solving Strategy #1
Engage in Successful Flailing!
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Notes­10.19 Distributive Property
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Notes­10.19 Distributive Property
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In the expression
3x + 4y – 7x + 5
There are four terms.
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Notes­10.19 Distributive Property
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x and y are different variables, so each of these is a different term.
x and x are the same, so they are called like terms. 11
Notes­10.19 Distributive Property
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The trick to subtraction is to remember that each number goes with the sign or operation that comes before it.
4x + 7y – 3x – 2y + 3z – 2y
Now collect like terms:
x + 3y + 3z
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Notes­10.19 Distributive Property
• 3x2 + 7xy + 5x2 + 3xy
October 19, 2015
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= 8x + 10xy
Remember x, x2, and x3 are different terms. You only combine like terms.
• 4x2 + 5x + 2x3 + 8x2 + 2x = 2x3 + 12x2 + 7x
By the commutative property we can rearrange multiplication, so xy = yx, these are like terms.
• 5xy + 3x + 4yx + 4y = 9xy +3x +4y
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X
X2
X
XY
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1
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Y2
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Notes­10.19 Distributive Property
October 19, 2015
x2 + 4x + 5 + 2x2 +2x + 3 X
X
X
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2
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X2
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X
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1
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X2
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Notes­10.19 Distributive Property
October 19, 2015
x2 + 4x + 5 + 2x2 +2x + 3 X
X
X
2
X
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1
1
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X2
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Notes­10.19 Distributive Property
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October 19, 2015
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2 x + 2x +2 + 3x + 2x + 4 + x
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X2
Y
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Y2
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The Distributive Property
5(x  9)
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Understanding the Distributive Property
2(x  3)
2 groups of x + 3
2( x  3)  2x  6
Understanding the Distributive Property
3(2 x  1)
3 groups of 2x +1
3(2 x  1)  6 x  3
Model using algebra tiles
2(3 x  4)
2 groups of 3x + 4
Model using algebra tiles
2(3 x  4)
2 groups of 3x + 4
 6x  8
Use the distributive property to simplify:
3(3x  1)
3(3 x)  3(1)
9x  3
Use the distributive property to simplify
7(2n  4)
7(2n)  4(7)
14n  28
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Use the distributive property to simplify
9(2x  3x  4)
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9(2x )  9(3x)  9(4)
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18x 27x 36
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