Calculadora de Expansão Binomial
Expanda expressões binomiais (a+b)^n. Calcule termos individuais.
Total
625.0000
Coeff6
Formula
Binomial Expansion
Binomial Theorem
(a + b)^n = sum of C(n,k) × a^(n-k) × b^k for k = 0 to n
Individual Term
The k-th term (0-indexed): C(n,k) × a^(n-k) × b^k
Example: (2 + 3)⁴ = 5⁴ = 625
Exemplo Resolvido
Find the k=2 term of (2+3)^4.
- 01C(4,2) = 6
- 02a^(4-2) = 2² = 4
- 03b^2 = 3² = 9
- 04Term value = 6 × 4 × 9 = 216
- 05(2+3)⁴ = 5⁴ = 625
Perguntas Frequentes
What is the binomial theorem?
The binomial theorem provides a formula for expanding (a+b)^n as a sum of terms involving powers of a and b, weighted by binomial coefficients.
How many terms in a binomial expansion?
(a+b)^n has exactly n+1 terms, corresponding to k = 0, 1, 2, ..., n.
What is the middle term?
When n is even, the middle term is at k = n/2. When n is odd, there are two middle terms at k = (n-1)/2 and k = (n+1)/2.
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