Transcript 1-5 The Distributive Property

Teacher note: The Commutative Property is the next lesson.
Therefore keep combining like terms simple! Cannot write in
good form because that requires commutative property.
For example 3 + 3x cannot be rewritten as 3x + 3
because that would require commutative property.
1-5 The Distributive Property
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
The Distributive Property
To distribute means to give something to each member
of a group. In algebra, the distributive property
means to distribute multiplication over addition or
subtraction.
a(b + c) = ab + ac
8(x + 5) = 8x + 8 • 5
= 8x + 40
a(b – c) = ab – ac
8(x – 5) = 8x – 8 • 5
= 8x - 40
It does not matter which side of the parentheses the
multiplier is on. 8(x + 5) is the same as (x + 5)8
Rewrite using the distributive property. Then simplify.
Write the problem.
Distribute.
Simplify.
3(x + 1)

3x + 3(1) optional step
3x + 3
An expression is simplified if it has: no grouping
symbols, no like terms, and no double signs.
Note: Good form dictates that a coefficient comes
before the variable in the answer.

5n
variable
coefficient 
Therefore, write 5n in your answer instead of n5.
If n was for notebooks,
you would say, “5
notebooks”. You would not
say, “notebooks 5”.
Rewrite using the distributive property. Then simplify.
Example 1
Example 2
5(y – 3)

5y – 5(3)
(x – 1)7

x7 – 1(7)
5y – 15
7x – 7
Example 5
1

24 x  
3

1
24x  24 
3
24x  8
Example 3
Example 4
1
6y  12  3

4
2 1
1
6
y
12
/  3/ / 3/
 
2y  4
(y + 2)─3
Example 6

 5 2x2  7 x

 
 5 2x2   5 7 x 
 10 x2  35x

y(─3) + 2(─ 3)
–3y + ─6
–3y – 6
Example 7
2
5
 9  y  
9
 3
2
5
 9  y    9  
 3 
 9
6y  5
Your answer must be simplified. Undo the double signs.
The Distributive Property
The Symmetric Property of Equality allow the
Distributive Property to be written as follows.
If a(b + c) = ab + ac then ab + ac = a(b + c)
If 8(x + 5) = 8 • x + 8 • 5 then 8 • x + 8 • 5 = 8(x + 5)
An algebraic expression is easier to evaluate when it
is simplified. The distributive property allows you to
combine like terms by adding their coefficients.
What is a term?
A term is a number or the product of a number and
variable/s.
one term
7
x
one term
7x
one term
1 7
one term
7
x x
two terms
7x
two terms
–– x
7+
Terms are
separated by
addition.
An algebraic expression is easier to evaluate when it is
simplified. The distributive property allows you to combine
like terms by adding their coefficients.
What is a coefficient?
In a term that is the product of a number and a variable,
the number is called the coefficient of the variable.
– 1 is the coefficient of x

–1x + 3x2

3 is the coefficient of x2
Like terms are terms in an expression that have
the same variable raised to the same power.
8x and 3x
4x2 and 4x
7m and –2m
Like Terms
Not Like Terms
Like Terms
25 and 10
Like Terms
Constants are
considered like
terms.
The problem.
Use the Identity Property
to name the coefficient.
Distribute.
Simplify.
4c – c
4c – 1c
– –
(4 – 1 )c
3c
If you have 4
cookies and you eat
a cookie, how many
cookies are left?
This is the
mathematical proof
for combining like
terms!
Simplify the expression.
2 + 9n2 + 10n
3n
—
—

(3 + 9)n2 + 10n
Write problem.
Distribute
Combine like terms.
12n2 + 10n
Like terms are terms in an expression that have
the same variable raised to the same power.
Copy in your
spiral
notebook!
Simplify – you must show your support work.
Example 8
17 a  21a
Example 9
12y2  8y2  6y
Example 10
5b2  3b
Example 11
2
5
x x x
6
6
Example 12
2
3
2x  x  x
3
4
Example 13
Example 14


4 a2  3ab  ab
3.7n  0.77n  9n
Example 15
Example 16
1
4x  16x  20y   7 x2  2 3x2  5x  1  9
4


Simplify – you must show your support work.
Example 8
17 a  21a
17  21a
Example 9
12y2  8y2  6y
Example 10
5b2  3b
12  8y2  6y
simplified
38a
4 y2  6y
Example 11
2
5
x x x
6
6
 1  2  5 x


 6 6
 6  2  5 x


6 6 6
13
x
6
Example 12
2
3
2x  x  x
3
4
 2  2  3 x


3 4

 24  8  9 x


 12 12 12 
41
x
12
Example 13
3.7n  0.77n  9n
3.7  0.77  9n
3.70  0.77  9.00n
13.47n
Simplify – you must show your support work.
Example 14


4 a2  3ab  ab
4a2  12ab  ab
2
4a  11ab
Example 15
1
4x  16x  20y 
4
Example 16


 7 x2  2 3x2  5x  1  9
4x  4x  5 y
 7 x2  6x2  10 x  2  9
8x  5y
 13x2  10 x  11
1-A7 Pages 30-31 #24-33,36-42,48-49,56-59.