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Binomial Theorem Calculator

Online binomial theorem: the term T_{k+1}=C(n,k)a^(n−k)b^k and the coefficients.

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T_(k+1)=C(n,k)a^(n−k)b^k
Power
Term k+1

📖 Tutorial | Binomial

1. Definition
The binomial theorem gives (a+b)^n=Σ C(n,k)a^(n−k)b^k; term k+1 has coefficient C(n,k).
2. Formula & Notation
n,kPower, term index
3. Properties & Laws
  • General term C(n,k)a^(n−k)b^k;
  • Coefficient sum 2^n;
  • Symmetric coefficients;
  • Matches Pascal triangle.
4. Steps
  1. Enter n,k;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: (a+b)^6, term 4 (k=3): C(6,3)=20, sum 64.
6. Common Pitfalls
k starts at 0;
Sum 2^n;
Middle term largest.

❓ FAQ | Binomial

Term?
C(n,k)a^(n−k)b^k.
Sum?
2^n.
Largest?
Middle.
Pascal's?
Triangle.
Example?
20.
(a−b)?
Alternating signs.