📐 Adding and Subtracting Polynomials Calculator
Add and subtract polynomials step by step
How to Use This Calculator
Enter First Polynomial
Type your first polynomial in standard form, e.g., 3x² + 2x + 1
Enter Second Polynomial
Type your second polynomial, e.g., x² + 4x + 2
Select Operation
Choose addition (+) or subtraction (-)
Calculate
See the expression and follow steps to combine like terms
Method
Combine like terms by adding or subtracting coefficients
Example 1: (3x² + 2x + 1) + (x² + 4x + 2)
Step 1: Write vertically or align like terms
3x² + 2x + 1
+ x² + 4x + 2
Step 2: Combine like terms
• x² terms: 3 + 1 = 4
• x terms: 2 + 4 = 6
• constants: 1 + 2 = 3
Result: 4x² + 6x + 3
Example 2: (5x² - 3x + 2) - (2x² + x - 1)
Step 1: Distribute the minus sign
5x² - 3x + 2 - 2x² - x + 1
Step 2: Combine like terms
• x² terms: 5 - 2 = 3
• x terms: -3 - 1 = -4
• constants: 2 + 1 = 3
Result: 3x² - 4x + 3
About Adding and Subtracting Polynomials Calculator
The Adding and Subtracting Polynomials Calculator helps you combine polynomials by adding or subtracting like terms. Like terms are terms with the same variable(s) raised to the same power. Polynomial addition and subtraction is fundamental in algebra and essential for solving more complex algebraic problems.
When to Use This Calculator
- Algebra Homework: Simplify polynomial expressions
- Polynomial Operations: Combine polynomials correctly
- Equation Solving: Prepare for solving polynomial equations
- Verification: Check your manual work
- Learning: Understand polynomial arithmetic
Why Use Our Calculator?
- ✅ Clear Steps: See how to combine like terms
- ✅ Both Operations: Addition and subtraction
- ✅ Educational: Learn polynomial manipulation
- ✅ Easy Format: Simple interface
- ✅ Free Tool: No registration required
Key Concepts
- Like terms have identical variable parts (same variables, same exponents)
- Add or subtract coefficients, keep variables unchanged
- Standard form: descending powers (highest degree first)
- For subtraction, distribute the minus sign to all terms
- Result should be simplified (no like terms remaining)
Tips for Success
- Always write polynomials in standard form first
- Line up like terms vertically if helpful
- For subtraction, carefully distribute the minus sign
- Double-check coefficients and signs
- Verify result is in standard form
Frequently Asked Questions
What are like terms?
Like terms 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.
How do I subtract polynomials?
Change the subtraction to addition by distributing the minus sign to all terms in the second polynomial, then combine like terms.
What is standard form?
Standard form orders terms from highest degree to lowest. Example: 4x³ - 2x² + x - 5 (not x - 5 - 2x² + 4x³).
Can I combine x² and x terms?
No! These are not like terms because they have different exponents. You can only combine terms with the same degree.