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( a + b ) n = a n + ( n 1 ) a n − 1 b + ( n 2 ) a n − 2 b 2 + … + ( n k ) a n − k b k + … + b n = ∑ k = 0 n ( n k ) a n − k b k {\displaystyle {\begin{aligned}(a+b)^{n}&=a^{n}+{\binom {n}{1}}a^{n-1}b+{\binom {n}{2}}a^{n-2}b^{2}+\ldots +{\binom {n}{k}}a^{n-k}b^{k}+\ldots +b^{n}\\&=\sum _{k=0}^{n}{\binom {n}{k}}a^{n-k}b^{k}\end{aligned}}}
