Expand (a + b)ⁿ without multiplying brackets out — Pascal's triangle gives the coefficients.
Theorem
(a+b)ⁿ = ∑ C(n,k) aⁿ⁻ᵏ bᵏ
Try it
(a+b)³
a³ + 3a²b + 3ab² + b³ — coefficients from Pascal's row 1, 3, 3, 1.
Expand (a + b)ⁿ without multiplying brackets out — Pascal's triangle gives the coefficients.
(a+b)³
a³ + 3a²b + 3ab² + b³ — coefficients from Pascal's row 1, 3, 3, 1.