Adding and Subtracting Polynomials Calculator
Add and subtract polynomials step by step
What are Polynomials?
A polynomial is an algebraic expression consisting of variables (usually x) and coefficients, where the variables are raised to non-negative integer powers. Examples include x², 3x + 2, and 5x³ - 2x + 1. The degree of a polynomial is the highest power of the variable in the expression.
How to Add and Subtract Polynomials
Follow these steps to add or subtract polynomials:
- Write the polynomials in standard form (descending powers)
- Align like terms (terms with the same variables and exponents)
- For addition: Combine like terms by adding their coefficients
- For subtraction: Change the signs of all terms in the second polynomial and then add
- Write the result in standard form
Understanding Like Terms
Like terms are terms in a polynomial that have the same variables raised to the same powers. Only like terms can be combined by adding or subtracting their coefficients.
Examples of like terms:
- 5x² and -3x²
- 7x and 2x
- 4 and -1 (constant terms)
Examples with Solutions
Example 1: Add (2x² + 3x - 1) + (x² - 2x + 4)
- Align like terms: 2x² + 3x - 1
- x² - 2x + 4
- Combine: (2x² + x²) + (3x - 2x) + (-1 + 4)
- Result: 3x² + x + 3
Example 2: Subtract (3x² - 2x + 1) - (x² + x - 2)
- Change signs: 3x² - 2x + 1
- -x² - x + 2
- Combine: (3x² - x²) + (-2x - x) + (1 + 2)
- Result: 2x² - 3x + 3
Common Mistakes to Avoid
- Combining terms that are not like terms (e.g., x² + x = x³)
- Forgetting to change all signs when subtracting polynomials
- Not properly aligning like terms before combining
- Incorrectly copying signs when rewriting the expression
- Forgetting to include all terms in the final answer