Algebra 1 Basic

Adding & Subtracting Polynomials

Combine two polynomials by choosing addition or subtraction. This tool matches like terms, distributes minus signs, and walks you through every step of the simplification.

Add or subtract any two polynomials
Color-coded like-term matching
Distributes minus sign automatically
Live
Polynomial Input
Use ^ for exponents: x^2, x^3. Supports integer and decimal coefficients.
Examples
Result
Enter two polynomials and press Calculate to see the result.
Simplified Polynomial
Degree
Terms in Result
Like-Term Groups
Step-by-Step Solution
Like Terms in Polynomials
3x² + x² = 4x²    but    3x² + x ≠ 4x³

Like terms are terms that share the same variable AND the same exponent (degree). Only the numerical coefficients can differ.

For example, 3x² and x² are like terms — both have variable x raised to the power 2. But 3x² and x are not like terms because the exponents differ (2 vs. 1). And 3x² + x does not simplify to 4x³ — you cannot add the exponents when combining like terms.

Constants (terms with no variable) are always like terms with each other.

When combining like terms, add or subtract the coefficients and leave the variable part unchanged. The exponent never changes.
Key Difference: Subtraction
(a − b + c) − (d + e − f) = a − b + c − d − e + f

When subtracting a polynomial, you must distribute the minus sign to every term inside the second set of parentheses — not just the first term.

Think of it as multiplying the second polynomial by −1: every positive term becomes negative, and every negative term becomes positive. Only after distributing should you group and combine like terms.

  • Addition: remove parentheses, signs stay the same.
  • Subtraction: remove parentheses, flip every sign in polynomial 2.
  • Then group like terms and combine coefficients.

Still mixing up like terms?

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