Multiplying Polynomials Calculator

Polynomial Multiplication Formula:

\[ \left(\sum_{i=0}^n a_i x^i\right) \times \left(\sum_{j=0}^m b_j x^j\right) = \sum_{i=0}^n \sum_{j=0}^m a_i b_j x^{i+j} \]

Product of Polynomials:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Polynomial Multiplication?

Polynomial multiplication is the process of multiplying two polynomials to produce a new polynomial. The product is obtained by multiplying each term of the first polynomial by each term of the second polynomial and then combining like terms.

2. How Does the Calculator Work?

The calculator uses the distributive property of multiplication:

\[ \left(\sum_{i=0}^n a_i x^i\right) \times \left(\sum_{j=0}^m b_j x^j\right) = \sum_{i=0}^n \sum_{j=0}^m a_i b_j x^{i+j} \]

Steps:

Parse each polynomial into its individual terms
Multiply each term from the first polynomial with each term from the second polynomial
Add the exponents of variables with the same base
Multiply the coefficients
Combine like terms in the result

3. Importance of Polynomial Multiplication

Applications: Polynomial multiplication is fundamental in algebra and has applications in computer science (polynomial interpolation), physics (wave equations), engineering (signal processing), and economics (modeling growth rates).

4. Using the Calculator

Instructions: Enter polynomials in standard form (e.g., "3x^2 + 2x + 1"). The calculator supports:

Positive integer exponents
Integer and decimal coefficients
Implied coefficients (e.g., "x" means "1x")
Single variable polynomials

5. Frequently Asked Questions (FAQ)

Q1: What is the degree of the product polynomial?
A: The degree is the sum of the degrees of the two polynomials being multiplied.

Q2: Can I multiply more than two polynomials?
A: Yes, by multiplying two at a time (associative property).

Q3: What about polynomials with multiple variables?
A: This calculator handles single-variable polynomials only.

Q4: How are negative coefficients handled?
A: Include the negative sign with the coefficient (e.g., "-2x^3").

Q5: What if I get an error message?
A: Check your input format and ensure you're using valid polynomial expressions.