Multiplying Polynomials Calculator
x
+
x
+
Result
How to Multiply Polynomials
To multiply polynomials:
- Multiply each term of the first polynomial by each term of the second polynomial
- Add the exponents of variables with the same base
- Combine like terms
(ax + b)(cx + d) = acx² + (ad + bc)x + bd
Example Problems
Example 1: (x + 2)(x² + 3x + 1)
Step 1: Multiply each term
- x × x² = x³
- x × 3x = 3x²
- x × 1 = x
- 2 × x² = 2x²
- 2 × 3x = 6x
- 2 × 1 = 2
Step 2: Combine like terms
Result: x³ + 5x² + 7x + 2
Example 2: (2x² - x + 3)(x + 1)
Step 1: Multiply each term
- 2x² × x = 2x³
- 2x² × 1 = 2x²
- -x × x = -x²
- -x × 1 = -x
- 3 × x = 3x
- 3 × 1 = 3
Step 2: Combine like terms
Result: 2x³ + x² + 2x + 3
Properties of Polynomial Multiplication
| Property | Description |
|---|---|
| Commutative | P(x) × Q(x) = Q(x) × P(x) |
| Associative | (P(x) × Q(x)) × R(x) = P(x) × (Q(x) × R(x)) |
| Distributive | P(x) × (Q(x) + R(x)) = P(x) × Q(x) + P(x) × R(x) |
Advertisement Space