What are Polynomial Operations?
Just like numbers, polynomials can be added, subtracted, and multiplied. These operations combine like terms (terms with the same variable and same exponent).
Rules for Adding and Subtracting Polynomials:
- Identify like terms (same variable and same exponent)
- Add or subtract the coefficients only
- Keep the variable part unchanged
Rules for Multiplying Polynomials:
- Use the distributive property: a(b + c) = ab + ac
- For binomial × binomial, use FOIL (First, Outer, Inner, Last)
- When multiplying, add exponents of like variables
FOIL Method for (a + b)(c + d):
- First: a × c
- Outer: a × d
- Inner: b × c
- Last: b × d
- Result: ac + ad + bc + bd
Vertical Multiplication Method:
Align terms by degree and multiply, just like multiplying multi-digit numbers.