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Pascal's triangle and the binomial theorem
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Learn it Row n of Pascal's triangle gives the coefficients of (a + b)ⁿ. In general (a + b)ⁿ = Σ C(n, k) aⁿ⁻ᵏ bᵏ. The term with bᵏ has coefficient C(n, k)·(numbers inside a and b raised to their powers).
Example: Find the coefficient of x³ in (2x + 1)⁵.
- Term: C(5, 3)(2x)³(1)² = 10 × 8x³.
- Coefficient 80.
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