Adding and Subtracting Polynomials

After studying this lesson, you will be able to:

• Add and subtract polynomials.

When adding and subtracting polynomials, remember that you can only add or subtract like terms. And, remember to add or subtract the coefficients - the exponents do not change.

Example 1

( 3y ² + 5y - 6 ) + (7y ² - 9 )

We are adding two polynomials so all we do is to collect like terms. It's a good idea to put the answer in descending order as we go.

Adding like terms the answer will be: 10y ² + 5y - 15

Example 2

( 4x ² -3y ² + 5xy ) - ( 8xy + 6x ² + 3y ² )

We are subtracting two polynomials so first we "add the opposite" in the second polynomial.

This will give us: ( 4x ² -3y ² + 5xy ) + ( - 8xy - 6x ² - 3y ² )

Now, we add like terms, beginning with the highest exponent so that our answer will be in descending order. Adding like terms the answer will be: -2x ² - 3xy - 6y ²