When adding polynomials, let's first remove the parentheses.  To do that, we use the distribution property.  The following 

can be written as

Then, we simply distribute the +1 through both polynomials.  We get

Now, we group and combine like terms. With polynomials, like terms are considered the terms with the same variables.  

For example, in the following

we have the variables  and .  We will group together all terms that contain  and all terms that contain , as well as any terms without variables. So, we get

Now, we combine the like terms.  We get

.

So, when we add the polynomials, the solution is

When solving a polynomial you must combine like terms. Like terms have the same degree value. A degree value is the number of exponents a term has.

When adding polynomials, we simply look at each term and combine like terms. Like terms in this case are terms that have the same variables. 

We can remove the parentheses in the problem, because doing so will not change the order of operations. So, we get

Now, we find like terms.

You can see all like terms have been highlighted in different colors. Now, we can combine them.

Note that we only add the coefficients together. Ther variables themselves do not change.

Writing that together, we get 

To solve this problem, we will group and combine like terms.  We can remove the parentheses because they do not change the answer. We get

Note that when you combine like terms, the variables do not change.  We only combine the coefficients. 

When adding polynomials, we can remove the parentheses because this does not have an effect on the answer. So,

becomes

Now, we combine like terms.  Like terms are considered terms with the same variables.  So,

where each different colored terms are like terms.  We combine them and get

Note that we do not change the variables when we add them, we only combine the coefficients.

Simplify the following expression:

Let's begin by putting like terms next to eachother:

Next, we keep the exponents the same (because we are only adding/subtracting), but we treat the numbers out in front just like regular subtraction or addition.

So our answer is

For this problem you need to combine your like terms.

  simplifies to  

But you must bring the other  over by subtraction so:

When finding our answer the first step is to get rid of the parentheses symbol so we can combine like terms, so we start with the following equation:

Then we have

We simple add like terms. Remember terms with the same power and variables can be added. So we have

The only term that will change from our original problem is the one linked to the variable m.

So then we have 

When subtracting polynomials, we must first distribute the negative through the second polynomial.

To do this, we simply take each term in the second polynomial times -1.  We get

We can remove the parentheses from the first polynomial.

Now, we combine like terms.  Like terms are the terms that have the same variables.  

The like terms have been highlighted.  When we combine them, we get

Multiply making sure to distribute the negative sign: