Calculator Inputs
Enter each polynomial in standard expanded form, such as 3x^2 - 2x + 5 or 0.5x^3 + x - 7.
Formula Used
If P(x) = Σ aixi and Q(x) = Σ bjxj, then:
This means every term in the first polynomial multiplies every term in the second. Terms with matching exponents are then added together.
How to Use This Calculator
- Enter Polynomial A in expanded form, such as 4x^3 - 2x + 1.
- Enter Polynomial B using the same variable and standard power notation.
- Choose the variable, sorting order, and display precision you prefer.
- Enable the step list when you want to review each distributive multiplication.
- Click Multiply Polynomials to view the product above the form.
- Use the CSV or PDF buttons to save the final tables and summary.
Example Data Table
| Example | Polynomial A | Polynomial B | Result |
|---|---|---|---|
| 1 | x + 2 | x + 3 | x^2 + 5x + 6 |
| 2 | 2x^2 - x + 4 | x - 5 | 2x^3 - 11x^2 + 9x - 20 |
| 3 | 0.5x^2 + x - 1 | 2x + 6 | x^3 + 5x^2 + 4x - 6 |
Frequently Asked Questions
1. What input style works best here?
Use expanded expressions with one variable, such as 3x^2 - 2x + 5. Write powers with the caret symbol, and avoid parentheses or factored forms.
2. Does the calculator combine like terms automatically?
Yes. After every pairwise multiplication, the calculator groups terms that share the same exponent and adds their coefficients into one simplified result.
3. Can I enter decimal coefficients?
Yes. Decimal coefficients such as 0.25x^3 or 1.5x are accepted. You can also control how many decimal places appear in the formatted output.
4. Can I choose a variable other than x?
Yes. You can switch between x, y, z, and t. Both polynomials must use the same selected variable for valid multiplication.
5. What does the pairwise multiplication table show?
It lists each term from Polynomial A against each term from Polynomial B, shows the resulting product term, and records the new exponent before combining.
6. Why might my expression fail to parse?
Parsing usually fails because of unsupported symbols, mixed variables, repeated carets, missing numbers after a decimal point, or factored expressions with parentheses.
7. What is included in the CSV and PDF exports?
Both exports include the input expressions, final product, summary metrics, combined coefficients, and the pairwise multiplication table generated from your current calculation.
8. Is polynomial multiplication related to convolution?
Yes. Matching polynomial coefficients multiply and combine according to exponent sums, which is the same structure used by discrete convolution in many applications.