How this calculator works
Distribute both terms of the first binomial across both terms of the second, then collect terms with equal exponents. Linear binomials produce a quadratic; general whole-number exponents may produce higher-degree polynomials. The displayed four coefficients help check signs before collection.
Formula
(a*x^n + b)(c*x^m + d) = ac*x^(n+m) + ad*x^n + bc*x^m + bd.
Worked example
(2x + 3)(4x - 5) gives 8x^2 - 10x + 12x - 15 = 8x^2 + 2x - 15. For (x^2 + 1)(x^2 - 1), the middle terms cancel, giving x^4 - 1.
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Frequently asked questions
What if the middle terms cancel?
Their sum becomes zero and that power is omitted from the simplified polynomial.
Can an exponent be negative?
This polynomial tool accepts only non-negative integer exponents. Negative exponents would make a Laurent expression.
How do I recover a missing factor?
Choose a recovery mode and enter the product coefficients and one known linear factor. A nonzero remainder or a quotient above degree one is rejected.