ELL Math
NOTES
Name _______________________
Topic: Distributive Property (SOL A.2)
Period _______ Date_________
Questions/Main Ideas
CLO: Apply the distributive property to simplify expressions.
Vocabulary:
Words to fill in the
blanks:
The Distributive Property is an algebra property which is used to multiply a
____________________ and two or more terms inside a set of_____________________.
For example,
single term
parentheses
2(3 + 6)
Steps:
12-
Add the numbers inside the parenthesis
Multiply by 2
2(3 + 6)
2(9)
18
binomial
BE CAREFUL
multiply
This example has a mistake in it. Look carefully and find out what is wrong.
2 (3 + 6)
2  3+6
6+6
12
unlike
Examine the expression:
6(2+4x)
The two terms inside the parentheses cannot be added because they are
___________________terms.
This is where the Distributive Property comes in.
6(2 + 4x)
remove
The Distributive Property tells us that we can __________________the parentheses if the
term outside the parentheses multiplies each of the terms inside.
tough:
This definition is tough to understand without a good example, so observe the example
below carefully.
6(2 + 4x)
Now by applying the Distributive Property…
6  2 + 6  4x
The parentheses are removed and each term inside the parentheses is multiplied by the six.
Now we can simplify the multiplication of the individual terms:
12 + 24x
Distributing a Negative Sign
negative
The next problem does not have a number outside the parentheses, only a
________________sign.
-(3 + x2)
inside
Outside the parenthesis you see a negative sign. That negative sign is really a
-1.
Make sure you multiply the signs first so you don’t get confused. Apply the rules!
negative times negative = positive
positive times positive = positive
positive times negative = negative
negative times positive = negative
The same rules apply for division!
+ ÷ + = +
- ÷ - = +
- ÷ + = - +÷ - = -
2
so, when you apply the distributive property in this example you get
=========================================================================
-3 – x
Distributing Variables
x(y + 1)
Consider the following example:
We can now apply the distributive property to the expression by multiplying each term
inside the parentheses by
x.
x

y+x

1
Now simplifying the multiplication, we get a final answer of:
xy + x
The same is true when a problem consists of a number, variables, and parentheses:
4x(x2 + 9)
Again, multiply each term inside the parentheses by the multiplier outside the parentheses.
4x  x2 + 4x  9
Then simplify:
4x3 + 36x
Let’s practice now!
1-
3 ( 4 + 5 ) = ______________________________________________
2-
2 ( a + 2 ) = ______________________________________________
3-
5 ( x – 3 ) = ______________________________________________
4-
-2 ( n + 5 ) = ______________________________________________
5-
-4 ( y – 2 ) = ______________________________________________
6-
- ( a + 3 ) = ________________________________________________________
7-
- ( x – 2 ) = ________________________________________________________
8-
4a ( a + 2 ) = _______________________________________________________
9-
-4a ( a – 2 ) = ______________________________________________________
10-
5x ( 2x + 3 ) = _____________________________________________________
11-
-2x - 3 ( -4x + 2) = __________________________________________________
12-
-5 + 2n (-3 – 2n) = ___________________________________________________
13-
2(3x – 6) -3 -4x (5 – 8x ) = _____________________________________________
14-
2m (3 – 4m – 7m + 5 ) = _______________________________________________
Challenging
x ( x-y) =
2m (-2m) =
2m + 2m =
5n ( 2n -3n )=
-b (4b+3b) =
15- 3b – 2 (-10b – 3b ) = ____________________________________________________
What do you think is the most important fact you have learned today?
________________________________________________________________________
________________________________________________________________________
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