 Related Topics:
Math Worksheets

In this lesson, we will look at how to add and subtract polynomials.

Adding polynomials involves combining like terms.

Example:

Add the polynomials 5x – 2 + y and –3y + 5x + 2

Solution:

5x – 2 + y + (–3y + 5x + 2)
= 5x + 5x + y – 3y – 2 + 2
= 10x – 2y

Example:

Find the sum of –7x3y + 4x2y2 – 2 and 4x3y + 1 – 8x2y2

Solution:

–7x3y + 4x2y2– 2 + 4x3y + 1 – 8x2y2
= –7x3y + 4x3y + 4x2y2– 8x2y2 – 2 + 1
= –3x3y – 4x2y2– 1

### Subtracting Polynomials

To subtract polynomials, remember to distribute the – sign into all the terms in the parenthesis.

Example:

Simplify –4x + 7 – (5x – 3)

Solution:

–4x + 7 – (5x – 3)
= –4x + 7 – 5x + 3
= –4x + 10

Example:

Simplify (5x2 + 2) – (– 4x2 + 7) + (– 3x2– 5)

Solution:

(5x2 + 2) – (– 4x2 + 7) + (– 3x2– 5)
= 5x2 + 2 + 4x2– 7 – 3x2– 5
= 5x2 + 4x2– 3x2 + 2 – 7 – 5
= 6x2– 10

How to add and subtract polynomials?
1. Combine like terms.
2. Write in descending order.
Example:
1. (4x2 + 8x - 7) + (2x2 - 5x - 12)
2. (5 + 24y3 - 7y2) + (-6y3 + 7y2 + 5)
3. (t2 - t + 5) + (7t2 - 4t - 20)

To subtract polynomials
1. Rewrite the subtraction as addition.
2. Combine like terms.
3. Write in descending order.
Example:
1. (4x2 + 8x - 7) - (2x2 - 5x - 12)
2. (6x4 + 3x3 - 1) - (4x3 - 5x + 9)
3. (1.5y3 + 4.8y2 + 12) - (y3 - 1.7y2 + 2y)
Examples of Adding and Subtracting Polynomials
Examples:
1. (2x5 - 6x3 - 12x2 - 4) + (-11x5 + 8x + 2x2 + 6)
2. (-9y3 - 6y2 - 11x + 2) - (-9y4 - 8y3 + 4x2 + 2x)
Adding polynomials and subtracting polynomials is essentially combining like terms of polynomial expressions. When adding and subtracting polynomials, they can either be arranged vertically or grouped according to degree. A knowledge of polynomial vocabulary is important before adding and subtracting polynomials. Multiplying monomials and binomials is another type of operation with polynomials.
Examples:
1. (4x2 - 3x + 2) + (5x2 + 2x - 7)
2. (5x3 + 7x2 - x) + (8x3 + 4x - 5)
3. (8x2 + 2x) - (10x2 + 2x - 9)
4. -(6x3 - 4x) - (2x3 + x2 -2x) Adding and Subtracting Polynomials
Examples:
1. (x2 + 4x + 5) + (6x + 3)
2. 2(x4 + 5x) - 6(x4 + 8x - 3)

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 