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(Expanding (a+b)^n)
The binomial theorem states: (a+b)^n = sum of C(n,k) × a^(n-k) × b^k for k from 0 to n.
Example: (a+b)^2 = C(2,0)a^2 + C(2,1)ab + C(2,2)b^2 = 1a^2 + 2ab + 1b^2 = a^2 + 2ab + b^2.
The coefficients 1, 2, 1 come from row 2 of Pascal's Triangle. Every binomial expansion uses a row of Pascal's Triangle as coefficients.
