1-6B Distributive Property and Combine Like Terms

1
1-6B Distributive Property and Combine Like Terms
Evaluate Algebraic Expressions
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
2
Do not use a calculator to complete homework.
Students who are calculator dependent tend to
make more calculating errors on tests.
After you finish an odd homework problem check
the answer in the back of the book. If the
answer is incorrect, investigate why it is wrong.
When students find their errors right away it is
more effective.
Dont skip steps. Write out the support work so
your eyes can see what your brain needs to
calculate. I did it in my head often leads to
errors.
Take notes in class, read the related lesson in
the text, and then review, review, review. Its
just not enough to sit in class for 45 minutes
and then hope you have absorbed it all.
Study tips
3
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.
4
Rewrite using the distributive property. Then
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.
5
Rewrite using the distributive property. Then
simplify.
The problem.
Change subtraction to addition.
1

Give the negative sign a multiplier of 1.
7y 25
Simplify.
What property justifies this step?
Copy in your spiral notebook!
6
Rewrite using the distributive property. Then
simplify.
Example 4
Example 5
Example 6
(m - 7)
(6 - y)
(2x - 15)

(m 7)
1


(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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Simplify the expression.
Example 8
Example 7
3(y 6) 5(4 - y) 7y2
Example 9
Example 10
a - b(b - 2a) 4b2
4y - (6y - 9)
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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)
a - b(b - 2a) 4b2

a b(b 2a) 4b2



4y (6y 9)




1
a

(-b)(-2a)

4b2
(-b)(b)

(-1)(6y)
4y

(-1)(-9)
a
b2

2ab
4b2
4y

6y

9
3b2
a
2ab
2y
9
Good form is alphabetical descending order!
Distribute the negative one.
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Evaluating Algebraic Expressions
An algebraic expression is easier to evaluate
when it is simplified. Simplify by using the
distributive property and then combine like
terms. Then use the value given to evaluate.
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Simplify and then evaluate when x 2.
Write the problem.
5x(2 - 3x) 7x
Change subtraction to addition.
5x(2 3x) 7x


Distribute.
10x
15x2

7x
Combine like terms.
3x

15x2
Substitute (dont forget to use parentheses).
3(2)

15(2)2
15(4) (3)(2)
Simplify.
60 6
66
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Simplify and then evaluate.
Example 11 when x 2
Example 12 when x 4
x(8 - x) 2x
6(-x - 3) - x(9 x)
x(8 x) 2x



6( x 3) x(9 x)




8x
x2

2x
6x

18

9x

x2
6x

x2
15x

18

x2
6(2)

(2)2
15(4)

18

(4)2
4 6(2)
16 15(4) 18
4 12
16 60 18
8
76 18
94
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Homework

• 1-A11 Handout A11