Related Topics:

More Lessons for Grade 6, Math Worksheets

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

### Adding Polynomials

### Subtracting Polynomials

### Videos

Adding and Subtracting Polynomials

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.
Adding and Subtracting Polynomials

You can use the free Mathway widget 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.

More Lessons for Grade 6, 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 5*x* – 2 + *y* and –3*y* + 5*x* + 2

**Solution:**

5*x* – 2 + *y *+ (–3*y* + 5*x* + 2)

= 5*x* + 5*x* + *y* – 3*y* – 2 + 2

= 10*x* – 2*y*

**Example:**

Find the sum of –7*x*^{3}*y* + 4*x*^{2}*y*^{2} – 2 and 4x^{3}y + 1 – 8*x*^{2}*y*^{2}

**Solution:**

–7*x*^{3}*y* + 4*x*^{2}*y*^{2}– 2 + 4x^{3}y + 1 – 8*x*^{2}*y*^{2}

= –7*x*^{3}*y* + 4x^{3}y + 4*x*^{2}*y*^{2}– 8*x*^{2}*y*^{2} – 2 + 1

= –3*x*^{3}*y* – 4*x*^{2}*y*^{2}– 1

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

**Example:**

Simplify –4*x* + 7 – (5*x* – 3)

* Solution*:

–4*x* + 7 – (5*x* – 3)

= –4*x* + 7 – 5*x* + 3

= –4*x* + 10

**Example:**

Simplify (5*x*^{2} + 2) – (– 4*x*^{2} + 7) + (– 3*x*^{2}– 5)

**Solution:**

(5*x*^{2} + 2) – (– 4*x*^{2} + 7) + (– 3*x*^{2}– 5)

= 5*x*^{2} + 2 + 4*x*^{2}– 7 – 3*x*^{2}– 5

= 5*x*^{2} + 4*x*^{2}– 3*x*^{2} + 2 – 7 – 5

= 6*x*^{2}– 10

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.

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 widget 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.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.