How this calculator works
FOIL names the four products: first, outer, inner and last. Each term in one binomial must multiply each term in the other. For general exponents, the first product has power n + m, while the two middle products have powers n and m. Equal exponents are combined, including a zero exponent that turns a term into a constant.
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.
Can I multiply more than two terms?
Use the multiplying polynomials calculator for longer coefficient lists.