Calcolatore Sviluppo Binomiale — 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

  • 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

    • Esempio Risolto

    Find the k=2 term of (2+3)^4.

    1. C(4,2) = 6
    2. a^(4-2) = 2² = 4
    3. b^2 = 3² = 9
    4. Term value = 6 × 4 × 9 = 216
    5. (2+3)⁴ = 5⁴ = 625