Binomial Expansion Calculator

The binomial theorem expands (a + b)ⁿ into n + 1 terms. The general term is Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ, where ⁿCᵣ comes from Pascal's triangle.

To find the coefficient of a particular power, write down the power of x in the general term, set it equal to the power you want and solve for r; r must be a whole number from 0 to n, or there's no such term.

$$(a+b)^n = \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^{r}$$

ⁿCᵣ

n! ÷ (r!(n − r)!)

Middle term

T(n/2 + 1) for even n; T((n+1)/2) and T((n+3)/2) for odd n