Line up like powers
For addition, combine coefficients attached to the same exponent. For subtraction, reverse every sign in the second polynomial before collecting terms, not just the first sign.
The constant is the coefficient of x⁰. Missing powers have coefficient zero, which is useful when organizing longer expressions in columns.
Multiply every pair of terms
Use the distributive property so each term in one polynomial multiplies every term in the other. Multiply coefficients and add exponents on x, then collect like powers.
The tool accepts degree up to 20 for each input, so a product may reach degree 40. It does not accept nested brackets or symbolic division; enter each expanded input separately.
Predict the leading term before expanding
For nonzero polynomials, the product degree is the sum of the input degrees. Multiplying a quadratic by a cubic should therefore produce a degree-five term, with coefficient equal to the product of the leading coefficients. Addition is different: leading terms can cancel, reducing the degree. This gives a quick structural check before verifying every coefficient.
LET’S WORK IT THROUGH
Subtract (x² − 4x + 1) from (3x² + 2x − 5).
- Reverse the second signs: −x² + 4x − 1.
- Combine squared and linear terms: 2x² + 6x.
- Combine constants: −5 − 1 = −6.
THE ANSWER2x² + 6x − 6.
YOUR TURN
A small check for understanding.
Multiply (x + 4)(x − 4).
Reveal the answer
x² − 16. The cross terms cancel.
Now try your own numbers.
The polynomial calculator includes input guidance and the limits of its supported calculations. Use it alongside the method above.
Open Polynomial calculator ↗A note on precision: preserve exact fractions where possible and round numerical results at the end. Found an unclear step? Prepare a correction report.