# Pre-Algebra : Adding and Subtracting Polynomials

## Example Questions

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### Example Question #1 : Adding And Subtracting Polynomials

Simplify:

Explanation:

Combine like terms:

### Example Question #2 : Polynomials

Simplify:

Explanation:

You can first rewrite the problem without the parentheses:

Next, write the problem so that like terms are next to eachother:

Then, add or subtract (depending on the operation) like terms. Remember that variables with different exponents are not like terms. For example, and are like terms, but and are not like terms:

### Example Question #2 : Adding And Subtracting Polynomials

Simplify:

Explanation:

When subtracting one polynomial from another, you must use distributive property to distribute the sign:

Now, rewrite the entire problem without the parentheses:

Reorganize the problem so that like terms are together. Remember that variables with different exponents are not like terms. For example, and  are like terms, but,  and  are not like terms:

Combine the like terms by adding or subtracting (depending on the operation):

### Example Question #3 : Adding And Subtracting Polynomials

Simplify:

Explanation:

First simplify the parentheses to get:

### Example Question #4 : Adding And Subtracting Polynomials

Simplify the expression:

Explanation:

To simplify the expression, combine like terms and eliminate the parentheses. Start by distributing the negative through the second parentheses.

Next, combine like terms.

### Example Question #5 : Adding And Subtracting Polynomials

Simplify the following expression:

Explanation:

In previous problems, we used combining like terms to simplify. In this case, we first need to distribute in order to get rid of the parentheses.

Parentheses always indicate the operation multiplication. You multiply the number on the ouside of the parenthese by EVERY term inside the parentheses. In this case, you would multiply  and

After this first step, you should have:

Then, we will combine like terms. Here, the like terms are and  (they both have the variable  and exponent 1). They combine into

### Example Question #1 : Polynomials

Simplify the following expression:

Explanation:

In previous problems, we used combining like terms to simplify. In this case, we first need to distribute in order to get rid of the parentheses.

Parentheses always indicate the operation multiplication. You multiply the number on the ouside of the parenthese by EVERY term inside the parentheses. In this case, you would multiply  and

After this first step, you should have:

Then, we will combine like terms. Here, the like terms are  and  (they both have the variable and exponent 1). They combine into

(There is not anything you need to combine the 12 with, so you just leave it as is.)

### Example Question #7 : Adding And Subtracting Polynomials

Simplify the following expression:

Explanation:

In previous problems, we used combining like terms to simplify. In this case, we first need to distribute in order to get rid of the parentheses.

Parentheses always indicate the operation multiplication. You multiply the number on the ouside of the parenthese by EVERY term inside the parentheses. In this case, you would multiply  and

After this first step, you should have:

Then, we will combine like terms. Here, the like terms are and (they both have no variable). They combine into

### Example Question #9 : Polynomials

Simplify the following expression:

Explanation:

The simplify this expression, combine like terms. Terms are like if they have the same variables and powers. To combine them, use addition and/or subtraction of the coefficients. The variables and powers do not change when you are combining.

and  are like terms (both have the variable  and the exponent 1). To combine them, you do

has the variable and the exponent 1.

has the variable  and the exponent 1

So  and  they are NOT like terms - their variables are different. We cannot combine them. If you cannot combine terms, just leave them the same as they are and re-write them in you answer.

### Example Question #10 : Polynomials

Simplify the following expression:

Explanation:

The simplify this expression, combine like terms. Terms are like if they have the same variables and powers. To combine them, use addition and/or subtraction of the coefficients. The variables and powers do not change when you are combining.

and  are like terms (both have the variable  and the exponent 1). To combine them, you do

has the variable  and the exponent 2.

has the variable  and the exponent 3.

So   and are NOT like terms - their exponents are different. We cannot combine them. If you cannot combine terms, just leave them the same as they are and re-write them in you answer.