Simplify the following expression

We can begin by grouping like terms:

Next, combine the like terms. In this case, simply treat them like two subtraction problems.

So our answer is:

When subtracting variables, you must first make sure you have the same variables.  So, in this case

we can see that both terms contain the variable x.  Therefore, we can subtract them. 

Now, when we subtract them, we can think of the variables as objects.  So, we can say that the variable x is actually pieces of pizza.  So,

is saying we have 9 pieces of pizza and we eat 3 pieces of pizza.  So how many pieces of pizza do we have left? 

We can simplify our problem the same way.

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

let's think of the variable y as pens.  So, we can look at the problem as we currently have 9 pens.  We let our friends borrow 3 pens.  How many pens do we have now? The answer is 6.  We now have 6 pens.  

We can subtract the variables in the same way.  So,

To subtract variables, we will look at the variables as objects.  So, 

we can look at it as the following.  We have 5 dollars.  We go to the store and buy something and spend 2 dollars.  How many dollars do we have now?  We now have 3 dollars.  We subtract variables in the same way. So

When solving this problem we need to remember our order of operations, or PEMDAS. 

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable  to a number, so we move to the next step. 

Multiplication: We can distribute (or multiply) the . 

Addition/Subtraction: Remember, we can't add a variable  to a number, so the  is left alone.

When solving this problem we need to remember our order of operations, or PEMDAS. 

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable  to a number, so we move on to the next step

Multiplication: We can distribute the negative sign to the  and 

Remember, a negative times a negative will equal a positive, so we have a 

Finally we can combine like terms

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

we can think of x as grapes.  So, we start with 10 grapes.  If we eat 2 grapes, how many grapes do we have now?  We have 8 grapes.  We can subtract variables the same way.

Simplify the following statement:

We have two terms, each with the same exponent. We can complete this problem by subtracting the coefficients just as we would do any other subtraction

So our answer is just

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

we will think of b as being balloons.  So we can read this problem as

So, if we have 8 balloons, and we give away 2 balloon, how many balloons do we have now?

We subtract variables the same way.  So,

We can look at this as we have 8 of something, if we subtract 2 of those somethings, how many do we have now?

When subtracting variables, we can look at the variables as objects, then subtract those objects.

We can think of the variable b as bananas. So, we can look at it as

We can think of it like this:  If we buy 9 bananas at the store, and we eat 2 bananas, how many bananas do we have now?  We have 7 bananas left. So,

We subtract variables the same way.