How to add polynomials - Algebra

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):

To solve, simply combine like terms by adding their coefficients. Thus,

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:

To simplify you combind like terms:

Answer:

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

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):

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

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:

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.