a(b + c) is equal to ab + ac.

(a) can't be zero and the numbers can't be irrational

Example #2

7(3+8) = 7(3) + 7(8)

Example

3 (4+7) = 3x4 + 3x7

Distributive Property

3(x+7)

The distributive property is also for subtraction

The distributive property says that when you have an equation

a(b - c) is equal to ab - ac.

Example #1

9(10-5) = 9(10) - 9(5)

Simplify

If we examine this expression we want to collect the like terms. The first term is 3x. If we search the equation we will see the only term with an x variable is 5x. So we can add 3x and 5x because they are positive which is 8x. Next we can collect the numbers 25 and 7 because the don't have variables. That equals 31. The (y) doesn't have a matching term so it is left alone. The simplified equation is

Simplify

9x-5-3x+8+2y

9x,-3x,-5 & 8

Distributive Property

Distributive Property

Combining Like Terms

**Distributive Property and Combining Like Terms**

Lets look at this. First If we start on the left. Our first step is to do PEMDAS. We add 4 + 7= 11. We then multiply 3 (11)= 33. Now we'll look at the second equation on the right. First let's multiply 3x4=12 and then 3x7=21. Next lets add the products 12 + 21= 33. These two answers equal each other.

#1: 3+8= 11

#2: 7(11)= 77

#1: 7(3)=21 and 7(8)=56

#2: 21 + 56 =77

Both answers equal to 77

#1: 10-5=5

#2: 9(5)=45

#1: 9(10)= 90

#2: 9(5)=45

#3: 90-45= 45

Both answers are equal to 45

We can also use with variables

#1: 3(x)= 3x

#2: 3(7)= 21

#3: 3x+21

We can't break it down any further because of the variable.

Combining Like Terms

Combining like terms is the process of grouping like numbers and variables (along with their signs +/-) together to further simplify the equation. In order to combine like terms the the variables must match and/or numbers must be the similar.

3x+25+5x+7+y

8x+31+y

The terms that we can combine

Terms we can't combine

2y

Terms we can

combine

3x,5x,25,7

The 9x combines with -3x which equals 6x

and the -5 combines with 8 which equals 3.

We can't combine the 2y so it is left alone. So

our simplified expression is

6x+2y+3

Rewriting the equation

When we rewrite the equation make sure we place the variables in alphabetical order and then place the numbers last.

3x+25+5x+7+y

Terms we can't combine

y

Practice

#1: 3(2+12)=

Step # 1 : 3(2)= 6 and 3(12)=36

Step # 2: Add the products together

6+36 = 42

The answer is 42

Simplify

#2: 4x+30-2x+5y-12=

4x+30-2x+5y-12

#1: Collect like terms:

4x,-2x,30

and

-12

#2: Collect unlike terms:

5y

#3: Combine like terms:

4x-2x

(we subtract because the sign in front of 2x is negative. And

30-12

for the same reason. We are left with 2x and 18

#4: Rewrite the expression with our remaining terms in alphabetical order:

2x+5y+18

3(2+12)

When a variable doesn't have a coefficient it is understood that the coefficient is 1.

7y+5-y

We can combine the 2y and the (y) we can act as if there is a 1 in front of it

#1: 7y-1y= 6y

#2: 6y+5

#3: 3(7x+4)-5x+3

3(7x+4)-5x+3

#1: We first use the distribute property: 3(7x)= 21x and 3(4)=12

The new equation is:

21x+12-5x+3

#2: We combine like terms:

21x

,

-5x

,

12

and

3

.

21x-5x=16x

and

12+3=15

#3: We rewrite the equation placing it in alphabetical order

Our answer is :

16x+15

In order to use the distributive property there can't be an operation in front of the parenthesis.

2+(5+9)=?

We can't use the distributive property because there is an (+) between the 2 and the ()

We just do the operations start inside () 5+9=14 then add 2 +12=14

The answer is

14

#4: 3+(5x-2)-3x+9

#1: We can't do the distributive property because there is a (+) in front of the parenthesis.

#2: We can't do the operation inside of the () because we can't complete the operation because of the variable (5x).

#3: We can combine the like terms

3,-2

&

9

along with

5x

and

-3x

3-2+9= 10

and

5x-3x=2x

#4: We now rewrite the equation with all of our combined terms (remember variables go first in alphabetical order)

2x+10

3+(5x-2)-3x+9