16B Commutative and Associative Properties

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1-6B Commutative and Associative Properties
For tomorrows lesson you will need a colored
pencil and a ruler!
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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A common error in distributing occurs when a
negative is involved with subtraction. To avoid
errors change subtraction to addition.
3(m - 5)
The problem.
Change subtraction to addition.

3(m 5)

?
3m

3(5)
Distribute.
3m 15
Simplify.
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3
Use the distributive property to simplify.
The problem.
Change subtraction to addition.
1

Give the negative sign a multiplier of 1.
7y 25
Simplify.
What property justifies this step?
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4
Use the distributive property to simplify.
Example 1
Example 2
Example 3
8(m - 9)
(3g - 8)(5)
8(x - 2y 3z)
8(m 9)


8(x 2y 3z)


(3g 8)(5)


?
?
8x

8(2y)

8(3z)
8m

8(9)
3g(5)

8(5)
8x 16y 24z
8m 72
15g 40
8x 16y 24z
Note Your answer must be simplified.
Undo the double signs.
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Use the distributive property to simplify.
Example 4
Example 5
Example 6
(m - 7)
(6 - y)
(2x - 15)

1
(m 7)


(6 y)

1

(2x 15)

1
?
?
1(m)

( 1)(7)
?
1(6)

( 1)(y)
(1)2x

(1)(15)
7
m

6

y
2x 15
Good form gives the variable term before the
constant!
Use good form! Do not write as -1m 7.
What property justifies this move?
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Simplify the expression.
An expression is simplified if it has no
grouping symbols, no like terms, and no double
signs.
Like terms are terms in an expression that have
the same variable raised to the same power.
In the answer, good form is alphabetical
descending order! Constants are last.
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Please do not confuse these types of problems.
x x x
3x
2x 2x 2x
6x
x x x
x3
2x 2x 2x
8x3
x
x
x
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Simplify the expression.
Write problem.
Change subtraction to addition.
5x2 7x 3x2 5x



8x2
Combine like terms.
8x2 (2x)
2x
8x2 2x
Undo the double signs.
Good form is alphabetical descending order!
Constants are last.
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9
Simplify the expression.
Example 7
Example 10
4y - (6y - 9)
Example 8
Example 11
3(y 6) 5(4 - y) 7y2
9x - 4(2x - 1)
Example 9
Example 12
1 - 4(1 - 2x)
a - b(b - 2a) 4b2
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Simplify the expression.
Example 8
Example 7
3(y 6) 5(4 - y) 7y2
3x2 5x 4x2 7x




3(y 6) 5(4 y) 7y2


7x2
12x
3(y)

3(6)
5(4)

5(-y)

7y2
7x2 12x
3y
18

20

5y
7y2
2y
7y2
38
Good form has the variables in alphabetical order
with the powers in descending order! Constants
are last.
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Simplify the expression.
Example 9
Example 10
4y - (6y - 9)
1 - 4(1 - 2x)
1 4(1 2x)




4y (6y 9)




1
1
(-4)(1)

(-4)(-2x)

(-1)(6y)
4y

(-1)(-9)
1
4

8x
4y

6y

9
8x
( 3)
2y
9
8x 3
Distribute the negative one.
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Simplify the expression.
Example 11
Example 12
9x - 4(2x - 1)
a - b(b - 2a) 4b2

a b(b 2a) 4b2



9x 4(2x 1)




a

(-b)(-2a)

4b2
(-b)(b)

(-4)(2x)
(-4)(-1)
9x
a
b2

2ab
4b2
9x

8x

4
a
2ab
3b2
4
x
Good form is alphabetical descending order!
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Homework

• 1-A11 Handout A11