what is the most common way to determine the expansion of (a+b)^n?

Question

part of the answer is a famous Mathmatician's name

Answer 1

Bionomial expansion

this has got n+1 terms

the terms are (nCk) a^kb^n-k where k varies from 0 to n

for example (a+b)^3
one term (3C0) a^0b^3 = b^3
another term (3C1)a^1b^2 = 3ab^2
another (3C2)a^2b^1 = 3a^2b
another (3c3)a^3b^0 = a^3

add them and get a^3+3a^2b+3ab^2+ b^3

(nCk) = n!/(k!(n-k)!)

The n'th line of the pascal triangle gives you the coeffiecients . Starting from 0.

Answer 2

the answer is the binomial theorem, but I have a feeling that you want me to say using Pascal's triangle... the two are virtually equivalent anyway though.

Answer 3

Pascal's triangle give you the coefficients.