ADV003 · Advanced mathematics · Classes 11–12 + B.Tech
Binomial theorem
The binomial theorem expands (a + b)ⁿ into n + 1 terms with coefficients C(n, k). The general term is C(n, k) aⁿ⁻ᵏ bᵏ.
(a + b)ⁿBinomial theorem
📐 Formula
(a + b)ⁿ = Σₖ C(n, k) aⁿ⁻ᵏ bᵏ; Tₖ₊₁ = C(n, k) aⁿ⁻ᵏ bᵏ
✏️ Worked example
(x + 1)⁵ = x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1.
🌍 Where it is used
Probability of k successes, approximations like 1.02¹⁰.
❓ Quick check
Coefficient of x² in (1 + x)⁴?
🏋️ Practice
EasyNumber of terms in (a + b)⁷?
Answer: 8
MediumMiddle term of (x + 1)⁶?
Answer: 20x³
ChallengeApproximate 1.01⁵ using two terms.
Answer: 1 + 5 × 0.01 = 1.05