Algebra
Polynomials
Adding and subtracting polynomials
20 practice questions
2 video lessons
Theory + worked examples
Theory
To add or subtract polynomials, combine like terms (same variable and power):
- Add: combine matching terms.
- Subtract: distribute the minus sign, then combine.
The minus sign applies to every term in the second polynomial.
Combine like terms.
Line up matching terms.
Combining like terms:
\[ax^n\pm bx^n=(a\pm b)x^n\]
Only same-power terms combine.
How to add or subtract
- Distribute a minus sign if subtracting.
- Group like terms.
- Add or subtract coefficients.
- Write in standard form.
Example 1 — Add
Add \((3x^2+2x)+(x^2-x)\).
Solution
Combine like terms.
| \((3x^2+x^2)+(2x-x)\) | \(=\) | \(4x^2+x\) |
Example 2 — Subtract
Subtract \((5x^2+3x)-(2x^2-x)\).
Solution
Distribute the minus, then combine.
| \(5x^2+3x-2x^2+x\) | \(=\) | \(3x^2+4x\) |
Example 3 — With constants
Add \((x^2-4)+(3x^2+x+7)\).
Solution
Combine each like group.
| \(=\) | \(4x^2+x+3\) |
Example 4 — Distribute the minus
Why distribute the minus sign when subtracting?
Solution
Because it applies to every term in the second polynomial.
Common pitfalls
Distribute the minus to every term.
Only combine like terms.
Keep the correct sign on each term.
Frequently asked questions
How do you add polynomials?
Combine like terms.
How do you subtract polynomials?
Distribute the minus sign, then combine like terms.
What are like terms?
Terms with the same variable and power.
Does subtracting change every sign?
Yes — the minus applies to the whole second polynomial.
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