When subtracting variables, we can think of the variables as objects.  So, in the problem

we can think of the variable c as cookies.  So, we can write it like

We can think of it like this:  There are 12 cookies on a plate.  We eat 2 of the cookies.  How many cookies are left?  There are 10 cookies left on the plate.

So, we get

We subtract variables the same way:

To subtract variables, we will think of the variables as objects. So, in the problem

we can think of the variable b as bottles of water.  So, we can write it like

We can think of it like this:  A cooler has 10 bottles of water.  You take 1 bottle of water from the cooler.  How many bottles of water are left in the cooler?  There are 9 bottles of water in the cooler.  So,

We subtract variables the same way:

To subtract variables, we will look at the variables like they are objects.  So, in the problem

we can think of the variable b as books.  So, we can write it like this:

We can read this as:  We have borrowed 7 books from the library.  We return 4 of those books to the library.  How many books do we have left?  We have 3 books.  So,

We can subtract variables the same way.  We get

When subtracting variables, we can look at the variables as objects.  So, in the problem

we can think of the variable c as crackers.  So, we can write the problem like this:

Now, we can read the problem like this:  We have a plate with 10 crackers.  We go and eat 4 of the crackers.  How many crackers are left on the plate?  There are 6 crackers.  So,

We can subtract variables the same way:

When subtracting variables, we can look at the variables like objects.  So, in the problem

we can think of the variable b as brownies.  So, we can write the problem like this:

We can read it like this:  You see there is a plate that contains 10 brownies.  You love brownies, so you eat 2 of them.  How many brownies are left on the plate?  There are 8 brownies left.

We can subtract variables the same way.

To subtract variables, we will look at the variables like they are objects.  So, in the problem

we can think of the variable c as cookies.  So, we can write it like this:

We can read it like this:  There is a plate with 10 cookies on it.  They smell delicious, so we decide to eat 4 cookies.  How many cookies are left on the plate?  There are 6 cookies left on the plate.

We can subtract variables the same way:

Begin by distributing the subtraction through the group:

Next, change the double negative to a positive:

Add the numbers and keep the variable:

Answer:

Add the numbers and keep the variable:

Answer:

In order to add variables the terms must be like. In order for terms to be like, the variables must be exactly alike also being raised to the same power by the exponent.

In this case the like terms are  and . Just because there is a 1 in the exponent for the first term doesnt mean it is different from the second term. With exponents if a variable does not show an exponent, that means it is still to the first power. 

We add the coefficients of the like terms. The coefficient is the number in front of the first variable, in this case it is 1 for both terms because of the identity property of multiplication stating any variable, term, or number multiplied by 1 is itself.

Our last term is not like because the  variable is raised to a different power than the other two. In this case we do not combine it to the like terms, we just add it to the end of the term.