Subtracting polynomials is understood as adding the additive inverse of the subtrahend: every term in the polynomial being subtracted changes sign, and only like terms—those with identical variable parts and exponents—are combined by adding their coefficients. This includes simplifying one-variable polynomials with integer or rational coefficients and whole-number exponents, supporting later work with equations and functions; polynomial division, multivariable generalizations, and abstract polynomial theory are outside this scope.
On this page:
- Learn “Subtract polynomials” with a detailed explanation of the concept
- Master “Subtract polynomials” with unlimited, free practice problems
- Download (or modify) a free worksheet on Subtract polynomials you can use at home or in class with practice problems that scaffold and explore “Subtract polynomials” from different perspectives.
- Start working on adaptive units like “Negative Integers - Intro” or “Algebra - Identify and Combine Like Terms” that introduce, teach, or practice “Subtract polynomials” to maximize your learning.
Detailed Explanation: Subtract polynomials
To subtract polynomials, change the sign of every term in the polynomial being subtracted. Then combine like terms.
Example:
Step 1: Change the signs in the second polynomial.
The subtraction sign applies to every term:
Step 2: Group like terms.
Like terms have the same variable and exponent:
Step 3: Combine the coefficients.
Therefore,
Remember: only combine like terms, such as with and with .
Learn by doing: Subtract polynomials
Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill
Your results
Practice with unlimited practice problems
Practice:
Like Terms - Combine - Order 2 - Whole - One Variable - Expression to Pair
Earned ?
Download/Modify Free Grade 9 'Subtract polynomials' Worksheet
Print this free 'Subtract polynomials' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Like Terms - Combine - Order 2 - Whole - One Variable - Expression to Pair
- Like Terms - Combine - Order 2 - Fractional - One Variable - Expression to Pair
- Negative Integer Subtraction - Intro
- Negative Integer Subtraction
Units Teaching This Skill
These adaptive units introduce, teach, or reinforce this skill (Subtract polynomials) through scaffolded problems that grow in difficulty as concepts are understood.