Polynomial Operations - Algebra

You must multiply out the first set of parenthesis (distribute) and you get 4x – x2. Then multiply out the second set and you get –3x + x2. Combine like terms and you get x.

x(4 – x) – x(3 – x)

4x – x2 – x(3 – x)

4x – x2 – (3x – x2)

4x – x2 – 3x + x2 = x

When simplifying polynomials, only combine the variables with like terms.

can be added to , giving .

can be subtracted from to give .

Combine both of the terms into one expression to find the answer:

This is not a FOIL problem, as we are adding rather than multiplying the terms in parentheses.

Add like terms to solve.

and have no like terms and cannot be combined with anything.

5 and -5 can be combined however:

This leaves us with .

This is not a FOIL problem, as we are adding rather than multiplying the terms in parenteses.

Add like terms to solve.

Combining these terms into an expression gives us our answer.

LCM of

LCM of

and since

The LCM

First factor the denominators which gives us the following:

The two rational fractions have a common denominator hence they are like "like fractions". Hence we get:

Simplifying gives us

Place like terms (with the same variable and exponent) together.

Add the like terms.

Add , , and .

Group like terms (with the same variable and exponent). Line up the polynomials in columns to make grouping the terms from several polynomials easier. Then add down.

Distribute the negative sign through all terms in the parentheses:

Add the second half of the expression, to get:

Subtract the first expression from the second to get the following:

This is equal to:

Combine like terrms:

To simplify you combind like terms:

Answer:

When combining polynomials, only combine like terms. With the like terms, combine the coefficients. Your answer is .

Don't be scared by complex terms! First, we follow our order of operations and multiply the into the first binomial. Then, we check to see if the variables are alike. If they match perfectly, we can add and subtract their coefficients just like we could if the expression was .

Remember, a variable is always a variable, no matter how complex! In this problem, the terms match after we follow our order of operations! So we just add the coefficients of the matching terms and we get our answer:

To solve , identify all the like-terms and regroup to combine the values.

To add two polynomials together, you combine all like terms.

Combining the terms gives us

Combining the terms gives us , since there is only 1 of those terms in the expression it remains the same.

Combining the terms gives us

and finally combining theconstants gives us

summing all these together gives us

To add polynomials, simply group by like terms and perform the indicated operation. Remember, only like-variables can be added to one another:

is the simplest form of this expression.

Collect like terms.

In order to simplify this expression, we need to add together like terms. What this means, is that we can only add together different parts of the expression that have the same kind of variable. For example, can only be added to other values that also have . We cannot combine to values that do not have the same exact variable - so, we cannot combine it with , or , and so on. Everything about the variables of two terms needs to be exactly the same if we are going to be able to combine them - the only thing that can be different are the coefficients (the numbers in front of the variables).

So, let's look at the expression above, and see if there are any like terms that we can combine.

Starting with - in order to be combined with this term, any other term must have as their variable. There is one other term in this expression tha thas as their variable - . If two terms hae the exact same variables, the only thing that we need to do in order to combine them is to add their coefficients together:

Now, let's look at the next term in the expression, . There are no other terms that have as their variable, so this term will stay the same.

Now, let's look at . There is one other term that has as their vairable: . Let's add these two terms together:

Finally, let's look at our last term which happens to have no variable: . There are no other terms in the expression that have no variable, so this term will stay the same.

Now, let's add together all of our simplified terms, as well as the terms that could not be simplified:

This is our simplified answer.

To solve this problem, first distribute anything through parentheses that needs to be distributed, then combine all terms with like variables (i.e. same variable, same exponent):