Math July 13, 2026 · 8 Min Read

Adding and Subtracting Polynomials Calculator – Guide & Formulas

Add and subtract polynomials step by step. Enter two polynomials and get the simplified result with like terms combined automatically.

Add and subtract polynomials step by step with our free calculator. Enter two polynomials, choose add or subtract, and get the simplified result instantly.

Key Takeaway

Use the free Adding and Subtracting Polynomials Calculator to add and subtract polynomials step by step. enter two polynomials and get the simplified result with like terms combined automatically. Get instant results with step-by-step explanations.

How to Use the Adding and Subtracting Polynomials Calculator

  1. Enter the first polynomial expression (e.g., 3x^2 + 2x - 5).
  2. Select the operation: Addition (+) or Subtraction (-).
  3. Enter the second polynomial expression.
  4. Review the combined result with like terms grouped and simplified.

The Formula

Addition: Add coefficients of matching powers. Subtraction: Subtract coefficients of matching powers. Always combine like terms (terms with the same variable and exponent).

Variable Definitions

  • Like Terms: Terms with the same variable raised to the same power
  • Coefficient: The numerical factor of a term
  • Degree: The highest exponent of the polynomial
  • Polynomial: An expression with variables raised to non-negative integer powers

Adding (3x² + 2x - 5) + (x² - 4x + 7)

Add two trinomials by combining like terms.

  1. Step 1: Group like terms: (3x² + x²) + (2x - 4x) + (-5 + 7).
  2. Step 2: Combine x² terms: 3x² + x² = 4x².
  3. Step 3: Combine x terms: 2x - 4x = -2x.
  4. Step 4: Combine constants: -5 + 7 = 2.
  5. Step 5: Result: 4x² - 2x + 2.

Frequently Asked Questions

What are like terms?

Like terms are terms that have the same variable(s) raised to the same power(s). For example, 3x² and 5x² are like terms, but 3x² and 3x are not. Only like terms can be combined by adding or subtracting their coefficients.

How do I subtract polynomials?

Distribute the negative sign to every term in the second polynomial, then add. For example, (2x + 3) - (x - 1) becomes 2x + 3 - x + 1 = x + 4.

What if the polynomials have different degrees?

Keep the terms of the higher-degree polynomial as they are. For example, (x³ + 2x) + (x + 1) = x³ + 3x + 1. The x³ term has no like term in the second polynomial.

Does the order matter when adding?

No. Polynomial addition is commutative, meaning (a + b) = (b + a). The result is the same regardless of order. However, subtraction is not commutative: (a - b) ≠ (b - a).

Can I add more than two polynomials?

Yes. Add them one pair at a time, or group all like terms across all polynomials and combine them at once. The result is the same.