Algebra 1
Ch 2.6 – The Distributive Property
Objective
 Students will use the distributive property
Before we begin…
 The distributive property is a key algebraic
concept that looks something like this:
3(x + 4)
 We will work with this property and its many
forms throughout this course…
 It is expected that you are able to recognize
and know how to work with this property…
 If you cannot recognize and work with the
distributive property you will not be
successful in this course…
The Distributive Property
 The distributive property states:
To multiply a number by a sum or difference,
multiply each number inside the parentheses
by the number outside the parentheses
 The distributive property can be used with
multiplication and addition or multiplication and
subtraction
 Let’s see what it looks like…
Example 1
5(3 + 2)
15 + 10 = 25
Proof: 5(3+2) = 5(5) = 25
Algebraic Expressions
 The distributive property can be used to
re-write algebraic expressions.
 Use the same process…multiply what’s
on the outside of the parenthesis by
each term within the parenthesis
 Let’s see what that looks like…
Example 2
3(x + 1)
3x + 3
Note: In this instance 3x and 3 are not like terms.
Therefore, you cannot combine them…so the expression
is simplified to just 3x + 3 – more on this later in the
lesson…
Distributive Property
 There are 2 ways that you can see the
distributive property
 With the multiplier on the left of the parenthesis
 With the multiplier on the right of the
parenthesis
Example:
5(2 + 3)
OR
(b + 3)5
In either event you multiply what’s on the
out side of the parenthesis with EACH
term inside the parenthesis
Comments
 Again…The distributive property is a
key algebraic concept…make no
mistake about it…you are REQUIRED
to be able to recognize and work with
the distributive property if you are to
pass Algebra 1!
Common Errors
 The most common error that students
make when working the distributive
property is that they only multiply what
on the outside of the parenthesis with
the first term within the parenthesis
 The other common error is that students
get the signs wrong…I do not give
partial credit for incorrect signs!
Example - Common Error
3(x - 1)
3x - 1
THIS IS INCORRECT!
Combining Like Terms
 In this course you will be expected to
simplify expressions by combining like
terms…
 In order to do that you have to be
familiar with the vocabulary and know
the definition of combining like terms…
 Let’s take a look at that…
Vocabulary
 Term – is the product of a number and a
variable. (product means to multiply)
 Examples:
3x
3x2
-x
-xy2
Three times x
Three times x squared
Negative 1 times x
Negative 1 times x times y
squared
Vocabulary
 Coefficient – the coefficient of a term is the
number in front of the variable.


If there is no number then the coefficient is
positive 1.
If there is no number and the variable is
negative then the coefficient is -1.
Examples:
-3x
x
-y
5y2
-3 is the coefficient
1 is the coefficient
-1 is the coefficient
5 is the coefficient
Vocabulary
 Like terms – are terms that have the same variable
and exponent. They can be combined by adding or
subtracting.
Examples:
5x + 3x
same variable raised to the same power.
They can be combined by adding to get 8x
5x2 – 3x2
same variable raised to the same power. They
can be combined by subtracting to get 2x2
5x + 3y
Different variables raised to the same power –
they cannot be combined
5x2 – 3x4
Same variable raised to different powers – they
cannot be combined
Vocabulary
 Constants – a number with no variable is
called a constant. Constant terms can be
combined by adding or subtracting.
Examples:
5x + 3 - 2
The constant terms are +3 and – 2.
They can be combined to get 5x + 1
- 7 + 6y - 2
The constant terms are – 7 and – 2.
They can be combined to get 6y – 9
Simplified Expressions
 An expression is considered simplified if it has
no grouping symbols and all the like terms have
been combined
Example:
-x2 + 5x - 4 - 3x + 2
- x2 cannot be combined with anything because there is no other squared
term
+ 5x and – 3x can be combined because they have the same variable and
exponent to get +2x
- 4 and + 2 are constant terms and can be combined to get – 2.
The simplified expression is:
-x2 + 2x - 2
Comments
 On the next couple of slides are some practice
problems…The answers are on the last slide…
 Do the practice and then check your answers…If you
do not get the same answer you must question what
you did…go back and problem solve to find the
error…
 If you cannot find the error bring your work to me and
I will help…
Your Turn
 Use the distributive property to rewrite the
expression without parenthesis
1. 3(x + 4)
2. - (y – 9)
3. x(x + 1)
4. 2(3x – 1)
5. (2x – 4)(-3)
Your Turn
 Simplify by combining like terms
6. 15x + (-4x)
7. 5 – x + 2
8. 4 + a + a
9. 8b + 5 – 3b
10. 9x3 – 2 – 4x3
Your Turn
 Apply the distributive property then simplify
by combining like terms
11. (3x + 1)(-2) + y
12. 4(2 – a) – a
13. - 4(y + 2) – 6y
14. -x3 + 2x(x – x2)
15. 4w2 – w(2w – 3)
Your Turn Solutions
1. 3x + 12
8. 4 + 2a
2. -y + 9
9. 5b + 5
3. x2 + x
10. 5x3 – 2
4. 6x – 2
11. -6x – 2 + y
5. -6x + 12
12. 8 – 5a
6. 11x
13. -10y – 8
7. 7 - x
14. -x3 + x2
15. 2w2 + 3w
Summary
 A key tool in making learning effective is being
able to summarize what you learned in a
lesson in your own words…
 In this lesson we talked about the distributive
property… Therefore, in your own words
summarize this lesson…be sure to include key
concepts that the lesson covered as well as
any points that are still not clear to you…
 I will give you credit for doing this
lesson…please see the next slide…
Credit
 I will add 25 points as an assignment grade for you working on
this lesson…
 To receive the full 25 points you must do the following:



Have your name, date and period as well a lesson
number as a heading.
Do each of the your turn problems showing all work
Have a 1 paragraph summary of the lesson in your own
words
 Please be advised – I will not give any credit for work submitted:



Without a complete heading
Without showing work for the your turn problems
Without a summary in your own words…
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Ch 2.6 The Distributive Property

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