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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 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.

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.

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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.

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