Multiplying Polynomials Calculator – Guide & Formulas
Multiply polynomials instantly. Enter any two polynomial expressions and see the expanded result with step-by-step distribution. Supports binomials, trinomials, and higher degrees.
Multiply any two polynomials instantly with our free calculator. Enter expressions like (2x² + 3x - 1)(x + 4) and see the expanded result with step-by-step distribution.
Key Takeaway
Use the free Multiplying Polynomials Calculator to multiply polynomials instantly. enter any two polynomial expressions and see the expanded result with step-by-step distribution. supports binomials, trinomials, and higher degrees. Get instant results with step-by-step explanations.
How to Use the Multiplying Polynomials Calculator
- Enter the first polynomial using standard notation (e.g., 2x^2 + 3x - 1).
- Enter the second polynomial (e.g., x + 4).
- Review the expanded polynomial result.
- Check the step-by-step distribution showing each term multiplication.
The Formula
Variable Definitions
- aₙ, bₘ: Leading coefficients of each polynomial
- cᵢ: Coefficient of xⁱ in the product
- Like terms: Terms with the same power of x that can be combined
- Degree: Highest power of x in a polynomial
Multiplying (2x + 3)(x² - x + 1)
Expand a binomial times a trinomial.
- Step 1: Distribute 2x: 2x · x² = 2x³, 2x · (-x) = -2x², 2x · 1 = 2x.
- Step 2: Distribute 3: 3 · x² = 3x², 3 · (-x) = -3x, 3 · 1 = 3.
- Step 3: Combine like terms: 2x³ + (-2x² + 3x²) + (2x - 3x) + 3.
- Step 4: Simplified result: 2x³ + x² - x + 3.
Frequently Asked Questions
How do I multiply polynomials?
Multiply every term in the first polynomial by every term in the second polynomial. Then combine like terms (terms with the same exponent). This is an extension of the FOIL method used for binomials.
What is the degree of the product polynomial?
The degree of the product equals the sum of the degrees of the two input polynomials. For example, multiplying a degree-2 polynomial by a degree-3 polynomial gives a degree-5 result.
Can I multiply more than two polynomials?
Yes. Multiply the first two, then multiply that result by the third, and so on. The calculator handles two at a time, but you can chain results.
What notation should I use for exponents?
Use ^ for exponents: x^2 for x², x^3 for x³. You can also write xx for x² if preferred, but the ^ notation is clearer.
How do I handle negative coefficients?
Enter them directly: -3x^2 + 2x - 1. The calculator handles sign distribution automatically during multiplication.
What if I enter an invalid expression?
The calculator will display an error message. Make sure your expression uses valid syntax: numbers, x, ^ for exponents, + and - for addition/subtraction.
Does this work with variables other than x?
This calculator uses x as the variable. For other variables, substitute mentally or treat x as your variable of interest.
How is this different from the binomial multiplying calculator?
The binomial calculator handles exactly (ax + b)(cx + d). This polynomial calculator handles any degree: trinomials, quartics, and beyond.