\( (a + b) ^{2} \)の展開公式は，\( \)
パスカルの三角形
$$\begin{aligned}\left( a+b\right) ^{2}=a^{2}+2ab+b^{2},\
\left( a+b\right) ^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}\end{aligned}$$
$$\begin{aligned}\left( a+b\right) ^{4}=\left( a+b\right) \times \left( a+b\right) ^{3}\
?=\left( a+b\right) \times \left( a^{3}+3a^{2}b+3ab^{2}+b^{3}\right) \
?=1a^{4}+3a^{3}b+3a^{2}b^{2}+ab^{3}\
+1a^{3}b+3a^{2}b^{2}+3ab^{3}+1b^{4}\
?=a^{4}+4a^{3}b+6a^{2}b^{2}+4ab^{3}+b^{4}\end{aligned}$$
$$\begin{aligned}a^{3}+3a^{2}b+3ab^{2}+b^{3}\
\dfrac{\left( x\right) a+b}{a^{4}+3a^{3}b+3a^{2}b^{2}+ab^{3}}\
\dfrac{a^{3}b+3a^{2}b^{2}+3ab^{3}+b^{4}}{a^{4}+4a^{3}b+6a^{2}b^{2}+4ab^{3}+b^{4}}\end{aligned}$$
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& 21 \\
\times) & 32 \\ \hline
& 42 \\
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<!DOCTYPE html>
<html lang=”ja”>
<head>
<meta charset=”UTF-8″>
<title>Document</title>
</head>
<body>
\begin{array}{rr}
& 21 \\
\times) & 32 \\ \hline
& 42 \\
& 63 \hspace{0.5em} \\ \hline
& 672
\end{array}
<script asyncsrc=”https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_CHTML”></script>
</body>
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二項定理
\begin{align*} (a + b)^{n} &= {}_n \mathrm{C}_k \ a ^{} b ^{} +{}_n \mathrm{C}_k \ a ^{} b ^{} + {}_n \mathrm{C}_k \ a ^{} b ^{} + \cdots \cdots + {}_n \mathrm{C}_k \ a ^{} b ^{} + \cdots \cdots + {}_n \mathrm{C}_k \ a ^{} b ^{} + {}_n \mathrm{C}_k \ a ^{} b ^{}\end{align*}
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