Polynomial Addition and Subtraction Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Polynomial Addition and Subtraction.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Adding or subtracting polynomials by combining like terms—terms with the same variable raised to the same power.
Think of like terms as the same type of object: 3x^2 and 5x^2 are both 'x^2 things,' so you can combine them into 8x^2, just like 3 apples plus 5 apples equals 8 apples. You cannot combine x^2 and x any more than you can add apples and oranges.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Only like terms (same variable and exponent) can be combined; everything else stays separate.
Common stuck point: When subtracting, the minus sign must be distributed to EVERY term in the second polynomial, not just the first.
Sense of Study hint: Rewrite the polynomials vertically, aligning like terms in columns, then add or subtract column by column.
Worked Examples
Example 1
easySolution
- 1 Step 1: Group like terms: (3x^2 + x^2) + (5x - 3x) + (-2 + 7).
- 2 Step 2: Combine: 4x^2 + 2x + 5.
- 3 Check: At x = 1: (3+5-2) + (1-3+7) = 6 + 5 = 11 and 4+2+5 = 11 ✓
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
hardRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.