Adding and Subtracting Polynomials
Combine like terms.
Key idea
Combine like terms.
In depth
Combine like terms. For subtraction, distribute the minus sign over every term of the second polynomial first. Align by degree to avoid mistakes.
Worked example
(3x² + 2x) − (x² − 5x + 1) = 2x² + 7x − 1.
Real-world uses
- Combining area or cost expressions for pieces of a design into one formula
Common mistake
Changing the sign of only the first term in the subtracted polynomial.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Adding and Subtracting Polynomials?
Combine like terms. It is a topic at the intermediate level in Algebra.
Where is Adding and Subtracting Polynomials used in real life?
Real-world examples: Combining area or cost expressions for pieces of a design into one formula.
What should I learn before Adding and Subtracting Polynomials?
Make sure you are comfortable with Polynomials: Terms and Degree, the previous topic in Algebra.
What is a common mistake with Adding and Subtracting Polynomials?
Changing the sign of only the first term in the subtracted polynomial.
How can I practise Adding and Subtracting Polynomials?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Adding and Subtracting Polynomials?
Move on to Multiplying Polynomials next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.