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(a+b)n=an+(n1)an−1b+(n2)an−2b2+…+(nk)an−kbk+…+bn=∑k=0n(nk)an−kbk{\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}}}