algebra
Polynomial Operations
Adding Polynomials
Combine like terms — terms with the same variable and exponent.
(3x² + 2x + 1) + (x² - 4x + 5)= 4x² - 2x + 6
Subtracting Polynomials
Distribute the negative, then combine like terms.
(5x² + 3x - 2) - (2x² - x + 4)= 5x² + 3x - 2 - 2x² + x - 4
= 3x² + 4x - 6
Multiplying Polynomials (FOIL)
For binomials: First, Outer, Inner, Last
(x + 2)(x + 3)= x·x + x·3 + 2·x + 2·3
= x² + 3x + 2x + 6
= x² + 5x + 6
💡Like Terms Quick Check
3x² and 5x² are like terms (same variable, same exponent). 3x² and 3x are NOT like terms (different exponents). Always match both the variable AND the exponent!
⚠️ Common Mistakes
- Adding exponents when adding terms (wrong!): 3x² + 2x² ≠ 5x⁴
- Forgetting to distribute the negative sign to all terms
- Missing terms when using FOIL — check you have 4 products!