# How to Add and Subtract Polynomials? (+FREE Worksheet!)

Learn how to add and subtract polynomials and how to combine like terms and simplify polynomials in this article.

## Step by step guide to solve adding and subtracting polynomials

• Adding polynomials is just a matter of combining like terms, with some order of operations considerations thrown in.
• Be careful with the minus signs, and don’t confuse addition and multiplication!

### Adding and Subtracting Polynomials – Example 1:

Simplify the expressions. $$(2x^3-4x^4 )-(2x^4-6x^3 )=$$

Solution:

First use Distributive Property for $$-(2x^4-6x^3 )= -2x^4+6x^3$$
$$(2x^3-4x^4 )-(2x^4-6x^3 )=2x^3-4x^4-2x^4+6x^3$$
Find “like” terms and combine them: $$2x^3+6x^3=8x^3$$, $$-4x^4-2x^4=-6x^4$$

Now simplify: $$2x^3-4x^4-2x^4+6x^3=-6x^4+8x^3$$

### Adding and Subtracting Polynomials – Example 2:

Add expressions. $$(x^3-2)+(5x^3-3x^2 )=$$

Solution:

Remove parentheses: $$(x^3-2)+(5x^3-3x^2 )=x^3-2+5x^3-3x^2$$
Combine like terms: $$x^3+5x^3=6x^3$$

Now simplify: $$x^3-2+5x^3-3x^2=6x^3-3x^2-2$$

### Adding and Subtracting Polynomials – Example 3:

Subtract. $$(4x^3+3x^4 )-(x^4-5x^3 )=$$

Solution:

First use Distributive Property for $$-(x^4-5x^3 )=-x^4+5x^3$$
$$(4x^3+3x^4 )-(x^4-5x^3 )=4x^3+3x^4-x^4+5x^3$$
Combine like terms: $$4x^3+5x^3=9x^3$$, $$3x^4-x^4=2x^4$$

Now simplify: $$4x^3+3x^4-x^4+5x^3=2x^4+9x^3$$

### Adding and Subtracting Polynomials – Example 4:

Add expressions. $$(2x^3-6)+(9x^3-4x^2 )=$$

Solution:

Remove parentheses: $$(2x^3-6)+(9x^3-4x^2 )=2x^3-6+9x^3-4x^2$$
Combine like terms: $$2x^3+9x^3=11x^3$$

Now simplify: $$2x^3-6+9x^3-4x^2=11x^3-4x^2-6$$

## Exercises for Adding and Subtracting Polynomials

### Simplify each expression.

1. $$\color{blue}{(2x^3 – 2) + (2x^3 + 2)}$$
2. $$\color{blue}{(4x^3 + 5) – (7 – 2x^3)}$$
3. $$\color{blue}{(4x^2 + 2x^3) – (2x^3 + 5)}$$
4. $$\color{blue}{(4x^2 – x) + (3x – 5x^2)}$$
5. $$\color{blue}{(7x + 9) – (3x + 9)}$$
6. $$\color{blue}{(4x^4 – 2x) – (6x – 2x^4)}$$

1. $$\color{blue}{4x^3 }$$
2. $$\color{blue}{6x^3 – 2}$$
3. $$\color{blue}{4x^2 – 5}$$
4. $$\color{blue}{– x^2 + 2x}$$
5. $$\color{blue}{4x}$$
6. $$\color{blue}{6x^4 – 8x}$$

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