Using the Polynomial Multiplication Calculator
Use this for binomial expansion or products of polynomials up to degree six each. Enter the coefficients from highest power to constant term. Retain a zero for each missing power so the expression is interpreted correctly.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- P coefficients, highest power first
- 1, 2, 1
- Q coefficients, highest power first
- 1, -1
Example result
- Product
- x^3 + x^2 − x − 1
- Product coefficients
- 1, 1, -1, -1
- Degree
- 3
- Steps
- Read P(x) = x^2 + 2x + 1 and Q(x) = x − 1. Distribute every term of P across every term of Q. Combine products with the same power of x. Highest-power-first coefficients: 1, 1, -1, -1. Product: x^3 + x^2 − x − 1.
Method and assumptions
Convolve the coefficient lists to distribute and combine like powers. Include zero coefficients for missing powers. Each polynomial supports degree up to 6, with integer coefficients from −10,000 to 10,000.
Reference: openstax.org — method and further reading
Check the answer in the original problem
After solving, substitute the result into the original equation or relationship where possible. This can catch a sign error or a coefficient entered in the wrong position. Keep the exact inputs available when comparing with another tool, since changing a coefficient or rounding an intermediate value can change the problem being solved.
Common question
Can I multiply more than two polynomials?
Multiply the first two, then reuse the output coefficients with the next polynomial if each input remains within the supported degree and coefficient limits. This tool expands products; it does not factor them.