Binomial Expansion Calculator
Calculate individual terms of the binomial expansion (a + b)^n. Shows the coefficient, power of a, and power of b for a specific term.
Total
625.0000
Formule
## 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 - k=0: C(4,0)×2⁴×3⁰ = 1×16×1 = 16 - k=1: C(4,1)×2³×3¹ = 4×8×3 = 96 - k=2: C(4,2)×2²×3² = 6×4×9 = 216 - k=3: C(4,3)×2¹×3³ = 4×2×27 = 216 - k=4: C(4,4)×2⁰×3⁴ = 1×1×81 = 81 - Total: 16 + 96 + 216 + 216 + 81 = 625
Exemple Résolu
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
Questions Fréquentes
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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