Adding Polynomials – Examples
To see the examples and solutions on polynomials, please scroll down. Then try your skills on the addition of polynomials by completing the exercises below. The answers and explanations are provided after the last exercise.
Adding Polynomials – Exercises
1) (6x2 + 9xy + 7y2) + (8x2 + 2xy + 5y2) = ?
2) (2x2 + 3xy + 5y2) + (2x2 – 6xy – 7y2) = ?
3) (3x3 – 5xy – 2y + 3y2) + (2x3 + 4x2 + 5x + 3y – 8xy – 9y2) = ?
4) (3a2 + 4ab + 2b2) + (7a2 – ab – 6b2) + (8a2 – 5ab – 4b2) = ?
5) (4x2 + 3xy + 6y + 7y2) + (3x2 + 7xy + 5x – 9y2) + (6x2 – 8y + 2xy) = ?
Adding Polynomials – Answers
Answer 1
1) The answer is: 14x2 + 11xy + 12y2
Step 1: Remove the parentheses.
(6x2 + 9xy + 7y2) + (8x2 + 2xy + 5y2) =
6x2 + 9xy + 7y2 + 8x2 + 2xy + 5y2
Step 2: Then put like terms together.
6x2 + 8x2 + 9xy + 7y2 + 8x2 + 2xy + 5y2 =
6x2 + 8x2 + 9xy + 7y2 + 2xy + 5y2 =
6x2 + 8x2 + 9xy + 2xy + 7y2 + 2xy + 5y2 =
6x2 + 8x2 + 9xy + 2xy + 7y2 + 5y2
Step 3: Then perform the operations to solve.
(6x2 + 8x2) + (9xy + 2xy) + (7y2 + 5y2) =
14x2 + 11xy + 12y2
Answer 2
2) The answer is: 4x2 – 3xy – 2y2
(2x2 + 3xy + 5y2) + (2x2 – 6xy – 7y2) =
2x2 + 3xy + 5y2 + 2x2 – 6xy – 7y2
Step 2: Then put like terms together.
2x2 + 2x2 + 3xy + 5y2 + 2x2 – 6xy – 7y2 =
2x2 + 2x2 + 3xy + 5y2 – 6xy – 7y2 =
2x2 + 2x2 + 3xy – 6xy + 5y2 – 6xy – 7y2 =
2x2 + 2x2 + 3xy – 6xy + 5y2 – 7y2
Step 3: Then perform the operations to solve.
(2x2 + 2x2) + (3xy – 6xy) + (5y2 – 7y2) =
4x2 – 3xy – 2y2
Answer 3
3) The answer is: 5x3 + 4x2 + 5x – 13xy – 6y2+ y
Step 1: Remove the parentheses.
(3x3 – 5xy – 2y + 3y2) + (2x3 + 4x2 + 5x + 3y – 8xy – 9y2) =
3x3 – 5xy – 2y + 3y2 + 2x3 + 4x2 + 5x + 3y – 8xy – 9y2
Step 2: Then put like terms together.
3x3 + 2x3 – 5xy – 2y + 3y2 + 2x3 + 4x2 + 5x + 3y – 8xy – 9y2 =
3x3 + 2x3 – 5xy – 2y + 3y2 + 4x2 + 5x + 3y – 8xy – 9y2 =
3x3 + 2x3 + 4x2 – 5xy – 2y + 3y2 + 4x2 + 5x + 3y – 8xy – 9y2 =
3x3 + 2x3 + 4x2 – 5xy – 2y + 3y2 + 5x + 3y – 8xy – 9y2 =
3x3 + 2x3 + 4x2 + 5x – 5xy – 2y + 3y2 + 5x + 3y – 8xy – 9y2 =
3x3 + 2x3 + 4x2 + 5x – 5xy – 2y + 3y2 + 3y – 8xy – 9y2 =
3x3 + 2x3 + 4x2 + 5x – 5xy – 8xy – 2y + 3y2 + 3y – 8xy – 9y2 =
3x3 + 2x3 + 4x2 + 5x – 5xy – 8xy – 2y + 3y2 + 3y – 9y2 =
3x3 + 2x3 + 4x2 + 5x – 5xy – 8xy – 2y + 3y2 + 3y – 2y – 9y2 =
3x3 + 2x3 + 4x2 + 5x – 5xy – 8xy + 3y2 + 3y – 2y – 9y2 =
3x3 + 2x3 + 4x2 + 5x – 5xy – 8xy + 3y2 – 9y2 + 3y – 2y – 9y2 =
3x3 + 2x3 + 4x2 + 5x – 5xy – 8xy + 3y2 – 9y2 + 3y – 2y
Step 3: Then perform the operations to solve.
(3x3 + 2x3 ) + 4x2 + 5x + (–5xy – 8xy) + (3y2 – 9y2) + (3y – 2y) =
5x3 + 4x2 + 5x – 13xy – 6y2+ y
Answer 4
4) The answer is: 18a2 – 2ab – 8b2
Step 1: Remove the parentheses.
(3a2 + 4ab + 2b2) + (7a2 – ab – 6b2) + (8a2 – 5ab – 4b2) =
3a2 + 4ab + 2b2 + 7a2 – ab – 6b2 + 8a2 – 5ab – 4b2
Step 2: Then put like terms together.
3a2 + 7a2 + 4ab + 2b2 + 7a2– ab – 6b2 + 8a2 – 5ab – 4b2 =
3a2 + 7a2 + 4ab + 2b2 – ab – 6b2 + 8a2 – 5ab – 4b2 =
3a2 + 7a2 + 8a2 + 4ab + 2b2 – ab – 6b2 + 8a2 – 5ab – 4b2 =
3a2 + 7a2 + 8a2 + 4ab + 2b2 – ab – 6b2 – 5ab – 4b2 =
3a2 + 7a2 + 8a2 + 4ab – ab + 2b2 – ab – 6b2 – 5ab – 4b2 =
3a2 + 7a2 + 8a2 + 4ab – ab + 2b2 – 6b2 – 5ab – 4b2 =
3a2 + 7a2 + 8a2 + 4ab – ab – 5ab + 2b2 – 6b2 – 5ab – 4b2 =
3a2 + 7a2 + 8a2 + 4ab – ab – 5ab + 2b2 – 6b2 – 4b2
Step 3: Then perform the operations to solve.
(3a2 + 7a2 + 8a2) + (4ab – ab – 5ab) + (2b2 – 6b2 – 4b2) =
18a2 – 2ab – 8b2
Answer 5
5) The answer is: 13x2 + 5x + 12xy – 2y2 – 2y
Step 1: Remove the parentheses.
(4x2 + 3xy + 6y + 7y2) + (3x2 + 7xy + 5x – 9y2) + (6x2 – 8y + 2xy) =
4x2 + 3xy + 6y + 7y2 + 3x2 + 7xy + 5x – 9y2 + 6x2 – 8y + 2xy
Step 2: Then put like terms together.
4x2 + 3x2 + 3xy + 6y + 7y2 + 3x2 + 7xy + 5x – 9y2 + 6x2 – 8y + 2xy =
4x2 + 3x2 + 3xy + 6y + 7y2 + 7xy + 5x – 9y2 + 6x2 – 8y + 2xy =
4x2 + 3x2 + 6x2 + 3xy + 6y + 7y2 + 7xy + 5x – 9y2 + 6x2 – 8y + 2xy =
4x2 + 3x2 + 6x2 + 3xy + 6y + 7y2 + 7xy + 5x – 9y2 – 8y + 2xy =
4x2 + 3x2 + 6x2 + 5x + 3xy + 6y + 7y2 + 7xy + 5x – 9y2 – 8y + 2xy =
4x2 + 3x2 + 6x2 + 5x + 3xy + 6y + 7y2 + 7xy – 9y2 – 8y + 2xy =
4x2 + 3x2 + 6x2 + 5x + 3xy + 7xy + 6y + 7y2 + 7xy – 9y2 – 8y + 2xy =
4x2 + 3x2 + 6x2 + 5x + 3xy + 7xy + 6y + 7y2 – 9y2 – 8y + 2xy =
4x2 + 3x2 + 6x2 + 5x + 3xy + 7xy + 2xy + 6y + 7y2 – 9y2 – 8y + 2xy =
4x2 + 3x2 + 6x2 + 5x + 3xy + 7xy + 2xy + 6y + 7y2 – 9y2 – 8y =
4x2 + 3x2 + 6x2 + 5x + 3xy + 7xy + 2xy + 6y + 7y2 – 9y2 – 8y + 6y =
4x2 + 3x2 + 6x2 + 5x + 3xy + 7xy + 2xy + 7y2 – 9y2 – 8y + 6y
Step 3: Then perform the operations to solve.
(4x2 + 3x2 + 6x2) + 5x + (3xy + 7xy + 2xy) + (7y2 – 9y2) + (–8y + 6y) =
13x2 + 5x + 12xy – 2y2 – 2y
Adding Polynomials – Examples of Addition of Polynomials
For problems on the addition of polynomials, you need to group like terms together.
Click here to see our post on grouping like terms.
Now look at the adding polynomials example that follows.
Instructions: Study the following adding polynomials example.
(x2 + xy + y2) + (3x2 – 4xy + 2y2) = ?
Answer: 4x2 – 3xy + 3y2
STEP 1: Remove the parentheses, paying attention to any negatives.
(x2 + xy + y2) + (3x2 – 4xy + 2y2) =
x2 + xy + y2 + 3x2 – 4xy + 2y2
STEP 2: Group the like terms together using sets of parentheses.
x2 + xy + y2 + 3x2 – 4xy + 2y2 =
x2 + 3x2 + xy + y2 + 3x2 – 4xy + 2y2 =
x2 + 3x2 + xy + y2 – 4xy + 2y2 =
x2 + 3x2 + xy – 4xy + y2 – 4xy + 2y2 =
x2 + 3x2 + xy – 4xy + y2 + 2y2 =
(x2 + 3x2) + (xy – 4xy) + (y2 + 2y2)
STEP 3: Perform the addition or subtraction of the terms inside each set of parentheses to solve.
(x2 + 3x2) + (xy – 4xy) + (y2 + 2y2) =
(4x2) + (–3xy) + (3y2) =
4x2 – 3xy + 3y2
Addition of Polynomials on Your Exam
You will see several problems on adding polynomials on your exam.
If you liked this post on examples of adding polynomials, you should also see our post on subtracting polynomials to review this skill.
Also note that problems on the addition of polynomials may involve adding expressions that contain a negative number.
Addition of Polynomials – Further Practice
If you have found these questions and examples on adding polynomials useful, you may also want to view our other posts on polynomials:
