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Multiplying two polynomials means distributing every term of one across every term of the other, then combining whatever ends up with matching powers of x. This tool handles that full convolution directly for polynomials up to degree 4.
How it works
Each coefficient of the first polynomial is multiplied by each coefficient of the second, with the resulting term's power of x equal to the sum of the two original powers; terms landing on the same power are then added together.
- Enter p₁: x⁴ coefficient (optional).
- Enter p₁: x³ coefficient (optional).
- Enter p₁: x² coefficient (optional).
- Enter p₁: x coefficient.
- Enter p₁: constant.
- Enter p₂: x⁴ coefficient (optional).
- Enter p₂: x³ coefficient (optional).
- Enter p₂: x² coefficient (optional).
- Enter p₂: x coefficient.
- Enter p₂: constant.
- Click Calculate to see your results.
Examples
Two binomials
(x+2)(x-3) = x²-x-6.
A binomial times a trinomial
(x+1)(x²-2x+3) = x³-x²+x+3.
Who should use it
- Algebra coursework on multiplying polynomials beyond simple binomials.
- Checking polynomial multiplication homework.
Industry applications
- Mathematics education
Advantages
- Handles arbitrary-degree polynomials (up to degree 4 each) via full distribution.
- Automatically combines like terms in the final answer.
Limitations
- Coefficients only — does not parse a typed expression like "x^2+2x-3".
Common mistakes to avoid
- Forgetting that every term of the first polynomial must be multiplied by every term of the second — not just matching positions.
Best practices
- For larger polynomials, organize partial products by their resulting power of x as you go, rather than combining everything at the very end.
Tips
- The constant term of the product is always the product of the two original constant terms — a quick partial check on your final answer.