Polynomials - Pre-Algebra

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:

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):

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 ). To combine them, you do

6 and 2 are also like terms (both have no variable). To combine them, you do .

You now have your simplified expression: which is the final answer.

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.

So the answer is:

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.

So the answer is:

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

So the final answer is

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

To solve you must first distribute the negative to the parentheses

Then you should combine like terms and you are left with

First simplify the parentheses to get:

Then combine like terms to get your answer of

First distribute the negative:

Group like terms, meaning terms that have the same variable and same exponent:

Add the like terms:

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

So the final answer is

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

Next, combine like terms.

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

So the final answer is

The first step is to write out as

The next step is to re-arrange the expression so it is ordered by exponential degree, as:

The final step is to sum together like terms and simplify the expression, as follows:

To simplify, we will combine like terms.

This has two terms with , and two terms with , so we will group those together:

Now we can add together the like terms. Remember that if a term doesn't have a coefficient \[number in front of it\], there is only one of them:

Combine the like terms (x's together and y's together).

Don't forget to distribute the negative sign through the parenthesis.

Distribute appropriate sign and simplify:

Rearrange into standard form(descending degree or powers):

When adding or subtracting polynomials with exponents, the value of the exponent never changes. The exponent does change when multiplying or dividing.

Start by categorizing each polynomial into groups according to the variable, then according to the like variable's exponent. Because and share a common variable AND exponent, you may add the coefficients:

However, because does not share the same variable, you may not subtract it from . Therefore, you leave the rest as is:

To simplify this expression, it is necessary to eliminate the parentheses grouping the terms. Distribute the negative signs. Double negative translate the sign to a positive.

The answer is .