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What is the Binomial Theorem formula for expanding $(a + b)^n$ for a positive integer $n$?

デッキ「Gaokao essentials: original practice」の単語カード。

解答

$(a + b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$, where $\binom{n}{k} = \frac{n!}{k!(n - k)!}$.

解説

The general $(k+1)$-th term in the expansion is $T_{k+1} = \binom{n}{k} a^{n-k} b^k$, frequently tested in Gaokao algebra questions.

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