%
%	gbb60166@gmail.com	https://unilab.gbb60166.jp/prekou/prekou.htm
%
% aspectratio= は 1610, 169, 149, 54, 32 の中から選べる（省略時は 43）
% C:\texlive\2024\texmf-dist\tex\latex\beamer\beamer.cls
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfpagemode=FullScreen},aspectratio=169]{beamer}
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfstartview={XYZ null null 8.00}},aspectratio=169]{beamer}
\documentclass[20pt,dvipdfmx,usepdftitle=false,aspectratio=169]{beamer}
% pdfの栞の字化けを防ぐ
%\AtBeginDvi{\special{pdf:tounicode EUC-UCS2}}
% テーマ
\usetheme{Copenhagen}
% navi. symbolsは目立たないが，dvipdfmxを使うと機能しないので非表示に
\setbeamertemplate{navigation symbols}{} 
\usepackage{bxdpx-beamer,pxjahyper,minijs}
%\usepackage{graphicx}
%\usepackage{tkokugo,furikana,tsayusen,shiika,sfkanbun,jdkintou,plext}
\usepackage{type1cm}
\usepackage[deluxe]{otf}
%\usepackage{tikzsymbols}
%\usepackage[dvipdfmx]{graphicx}%
\def\pgfsysdriver{pgfsys-dvipdfmx.def}%（graphicxパッケージを使用しない場合はこの行を有効に）
%\def\pgfsysdriver{pgfsys-dvips.def}%デフォルト
%\usepackage[e]{esvect}
\usepackage{tikz}%（これで、pgfとpgfforが読み込まれます。）
%\usepackage{tikz-3dplot}
\usetikzlibrary{calc}
%\usetikzlibrary{arrows.meta,patterns,angles,intersections,backgrounds}
%\usepackage{animate}
%\usepackage{pgfplots}
%\pgfplotsset{compat=newest}
%\pgfplotsset{compat=newest, every axis/.append style={line width=1pt}}
%\PassOptionsToPackage{dvipdfmx}{graphicx}
\nofiles

\hypersetup{% Jul 18 2023
	pdftitle={プレ高数学科（LaTeX Beamer で汎用PDFプレゼンを作る）},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/prekou/prekou.htm}
	}

% フォントはお好みで
%\usepackage{txfonts}

\mathversion{bold}
\renewcommand{\familydefault}{\sfdefault}
\renewcommand{\seriesdefault}{bx}
\renewcommand{\kanjifamilydefault}{\gtdefault}
\renewcommand{\kanjiseriesdefault}{bx}
\setbeamerfont{title}{size=\normalsize,series=\bfseries}
\setbeamerfont{frametitle}{size=\normalsize,series=\bfseries}
\setbeamertemplate{frametitle}[default][center]
\usefonttheme{professionalfonts}

% 参考にしたURL
% http://windom.phys.hirosaki-u.ac.jp/fswiki/wiki.cgi?page=LaTeX+Beamer%A4%C7%A5%D7%A5%EC%A5%BC%A5%F3%A5%C6%A1%BC%A5%B7%A5%E7%A5%F3

\newcommand{\Slash}[1]{\ooalign{\hfil\kern-3pt／\hfil\crcr$#1$}}
\everymath{\displaystyle}

\newcommand{\maruwaku}[1]{\begin{tikzpicture}[scale=0.7, baseline={([yshift=-22pt] current bounding box.north)}]
\filldraw[color=CUDBlue, line width=1pt, rounded corners=2pt] (-0.1,0)--(2.1,0)--(2.1,1.1)--(-0.1,1.1)--cycle;
\draw(1,0.5) node[white]{#1};
\end{tikzpicture}
}

\setbeamersize{text margin left=5mm,text margin right=5mm}
\fboxrule=0.8pt

\makeatletter
\newcommand{\hooklen}[2]{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
%■等号付き不等号 by 美文書作成入門
\newcommand{\myleqq}{\mathrel{\mathpalette\gl@align<}}
\newcommand{\mygeqq}{\mathrel{\mathpalette\gl@align>}}
\newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
	\ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\makeatother

% カラーユニバーサルデザインを調べたつもりだがあまり自信がありません
% http://www.fukushihoken.metro.tokyo.jp/kiban/machizukuri/kanren/color.files/colorudguideline.pdf
% http://jfly.iam.u-tokyo.ac.jp/colorset/

% ■ アクセントカラー小面積を目立たせる高彩度色
\definecolor{CUDRed}{RGB}{255,75,0}
\definecolor{CUDGreen}{RGB}{3,175,122}
\definecolor{CUDBlue}{RGB}{0,90,255}
\definecolor{CUDCyan}{RGB}{77,196,255}
\definecolor{CUDMagenta}{RGB}{153,0,153}
\definecolor{CUDYellow}{RGB}{255,241,0}
\definecolor{CUDBrown}{RGB}{128,64,0}

\definecolor{CUDOrange}{RGB}{246,170,0}

% ■ ベースカラー広い面積の塗り分けに用いる低・中彩度色
\definecolor{CUDPink}{RGB}{255,202,191}
\definecolor{CUDBrightGreen}{RGB}{119,217,168}
\definecolor{CUDLime}{RGB}{216,242,85}
\definecolor{CUDCream}{RGB}{255,255,128}
\definecolor{CUDBrightCyan}{RGB}{191,228,255}
%\definecolor{CUD}{RGB}{}%

\setbeamercolor{CUDBrightGreen}{fg=black,bg=CUDBrightGreen!50}
\setbeamercolor{CUDBrightCyan}{fg=black,bg=CUDBrightCyan}
\setbeamercolor{CUDCream}{fg=black,bg=CUDCream!75}

%\setbeamercolor{frametitle}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{palette primary}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{frametitle}{bg=CUDOrange}
%\setbeamercolor{palette primary}{bg=CUDOrange}
\setbeamercolor{frametitle}{bg=CUDCyan!25,fg=black}
\setbeamercolor{palette primary}{bg=CUDCyan!25,fg=black}
%\setbeamercolor{frametitle}{bg=CUDCream!75,fg=black!80}
%\setbeamercolor{palette primary}{bg=CUDCream!75,fg=black!80}

\newcommand{\myfrac}[2]{\mathchoice%■ 修正 Oct 8,2023
	{%\fontsize{20}{20}\selectfont%	\displaystyle
		\frac{\raisebox{-.6ex}{\(#1\)}}{\raisebox{.4ex}{\(#2\)}}}%
	{\textstyle{\frac{#1}{#2}}}%	\textstyle
	{%\fontsize{13}{13}\selectfont%	\scriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	{%\fontsize{11}{11}\selectfont%	\scriptscriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	}


\begin{document}

\title{プレ高数学科}\author{gbb60166}
% 昔書いたコードでいろいろ気づきはあるが手直しする気力が起きません
\newcommand{\drawarrow}{\draw[CUDLime](\i)++(-0.25,0.25)--++(0,-1.5)
			--++(-0.2,0)--++(0.45,-0.5)--++(0.45,0.5)
			--++(-0.2,0)--++(0,1.5)--cycle;
	\draw(\i)++(0,-0.3) node{\( \times \)}
		(\i)++(0,-0.9) node{\( \times \)};
	}

\newcommand{\drawpascal}{\draw[line width=16pt,
		CUDBrightGreen!75,line cap=round]
		($ ({4*sqrt(2)/2},{4*sqrt(2)/2}) $)--($ (13,{4*sqrt(2)/2}) $)
			 node[black,xshift=-2em]{\small$(\kern1.3em)^2$に対応}
		%($ ({3*sqrt(2)/2},{3*sqrt(2)/2}) $)--($ (13,{3*sqrt(2)/2}) $)
		%	 node[black,xshift=-2em]{\small$(\kern1.3em)^3$に対応}
		%($ ({2*sqrt(2)/2},{2*sqrt(2)/2}) $)--($ (13,{2*sqrt(2)/2}) $)
		%	node[xshift=-5em]{\small$(\kern1.3em)^4$に対応}
		%($ ({sqrt(2)/2},{sqrt(2)/2}) $)--($ (13,{sqrt(2)/2}) $)
		%	node[xshift=-5em]{\small$(\kern1.3em)^5$に対応}
		(0,0)--(13,0)
			node[black,xshift=-2em]{\small$(\kern1.3em)^6$に対応};
	\draw[CUDYellow](0,0)--($ ({3*sqrt(2)},{3*sqrt(2)}) $)
				--($ ({6*sqrt(2)},0) $);
	\foreach \i in {1,...,5}{
		\draw[CUDYellow]($ ({\i*sqrt(2)/2},{\i*sqrt(2)/2}) $)
			--($ ({\i*sqrt(2)},0) $)
			--($ ({(\i+6)*sqrt(2)/2},{(6-\i)*sqrt(2)/2}) $);
		}
	\begin{scope}[CUDBlue]
	\foreach \i in {0,...,6}
		{\draw($ ({\i*sqrt(2)/2},{\i*sqrt(2)/2}) $) node{$1$};}
	\foreach \i in {7,...,12}
		{\draw($ ({\i*sqrt(2)/2},{(12-\i)*sqrt(2)/2}) $) node{$1$};}
	\draw($ ({6*sqrt(2)/2},{4*sqrt(2)/2}) $) node{$2$};
	\draw($ ({5*sqrt(2)/2},{3*sqrt(2)/2}) $) node{$3$};
	\draw($ ({7*sqrt(2)/2},{3*sqrt(2)/2}) $) node{$3$};
	\draw($ ({4*sqrt(2)/2},{2*sqrt(2)/2}) $) node{$4$};
	\draw($ ({6*sqrt(2)/2},{2*sqrt(2)/2}) $) node{$6$};
	\draw($ ({8*sqrt(2)/2},{2*sqrt(2)/2}) $) node{$4$};
		\draw($ ({3*sqrt(2)/2},{sqrt(2)/2}) $) node{$5$};
		\draw($ ({5*sqrt(2)/2},{sqrt(2)/2}) $) node{$10$};
		\draw($ ({7*sqrt(2)/2},{sqrt(2)/2}) $) node{$10$};
		\draw($ ({9*sqrt(2)/2},{sqrt(2)/2}) $) node{$5$};
		\draw($ ({2*sqrt(2)/2},0) $) node{$6$};
		\draw($ ({4*sqrt(2)/2},0) $) node{$15$};
		\draw($ ({6*sqrt(2)/2},0) $) node{$20$};
		\draw($ ({8*sqrt(2)/2},0) $) node{$15$};
		\draw($ ({10*sqrt(2)/2},0) $) node{$6$};
	\end{scope}
	}


%■■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■■


%\end{document}
%■■■■■■■■■■■■■　完成品　■■■■■■■■■■■■■■

\begin{frame}[t]
\frametitle{\( (a+b)^4 \)を計算しなさい}
普通、教科書や参考書には\({}_4 {\rm C}_2\)などを使った公式が書いてあるが、
パスカルの三角形を使ったやり方の方が簡単だと思う。\pause

\bigskip
パスカルの三角形とは、上の$2$つをたし算してできる図のことだ。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{パスカルの三角形}
\begin{tikzpicture}[rotate=0,scale=1,line width=2pt]
\visible<8->{\begin{scope}
		\small
		\draw[line width=16pt,CUDBrightGreen!75,
			line cap=round,	text=black]
		($ ({4*sqrt(2)/2},{4*sqrt(2)/2}) $)--($ (13,{4*sqrt(2)/2}) $)
			node[xshift=-2.2em]{\( (\kern1.3em)^2 \)に対応}
		($ ({3*sqrt(2)/2},{3*sqrt(2)/2}) $)--($ (13,{3*sqrt(2)/2}) $)
			node[xshift=-2.2em]{\( (\kern1.3em)^3 \)に対応}
		($ ({2*sqrt(2)/2},{2*sqrt(2)/2}) $)--($ (13,{2*sqrt(2)/2}) $)
			node[xshift=-2.2em]{\( (\kern1.3em)^4 \)に対応}
		($ ({sqrt(2)/2},{sqrt(2)/2}) $)--($ (13,{sqrt(2)/2}) $)
			node[xshift=-2.2em]{\( (\kern1.3em)^5 \)に対応}
		(0,0)--(13,0) node[xshift=-2.2em]{\( (\kern1.3em)^6 \)に対応};
	\end{scope}
	}
\draw[CUDYellow](0,0)--($ ({3*sqrt(2)},{3*sqrt(2)}) $)--($ ({6*sqrt(2)},0) $);
\foreach \i in {1,...,5}{
	\draw[CUDYellow]($ ({\i*sqrt(2)/2},{\i*sqrt(2)/2}) $)
		--($ ({\i*sqrt(2)},0) $)
		--($ ({(\i+6)*sqrt(2)/2},{(6-\i)*sqrt(2)/2}) $);
	}
\begin{scope}[CUDBlue]
\foreach \i in {0,...,6}{\draw($ ({\i*sqrt(2)/2},{\i*sqrt(2)/2}) $) node{$1$};}
\foreach \i in {7,...,12}
	{\draw($ ({\i*sqrt(2)/2},{(12-\i)*sqrt(2)/2}) $) node{$1$};}
\visible<2>{\draw($ ({6*sqrt(2)/2},{5*sqrt(2)/2}) $) node{$+$};}
\visible<2->{\draw($ ({6*sqrt(2)/2},{4*sqrt(2)/2}) $) node{$2$};}
\visible<3>{\draw($ ({5*sqrt(2)/2},{4*sqrt(2)/2}) $) node{$+$};}
\visible<3->{\draw($ ({5*sqrt(2)/2},{3*sqrt(2)/2}) $) node{$3$};}
\visible<4>{\draw($ ({7*sqrt(2)/2},{4*sqrt(2)/2}) $) node{$+$};}
\visible<4->{\draw($ ({7*sqrt(2)/2},{3*sqrt(2)/2}) $) node{$3$};}
\visible<5>{\draw($ ({4*sqrt(2)/2},{3*sqrt(2)/2}) $) node{$+$};}
\visible<5->{\draw($ ({4*sqrt(2)/2},{2*sqrt(2)/2}) $) node{$4$};}
\visible<6>{\draw($ ({6*sqrt(2)/2},{3*sqrt(2)/2}) $) node{$+$};}
\visible<6->{\draw($ ({6*sqrt(2)/2},{2*sqrt(2)/2}) $) node{$6$};}
\visible<7->{\draw($ ({8*sqrt(2)/2},{2*sqrt(2)/2}) $) node{$4$}
		($ ({3*sqrt(2)/2},{sqrt(2)/2}) $) node{$5$}
		($ ({5*sqrt(2)/2},{sqrt(2)/2}) $) node{$10$}
		($ ({7*sqrt(2)/2},{sqrt(2)/2}) $) node{$10$}
		($ ({9*sqrt(2)/2},{sqrt(2)/2}) $) node{$5$}
		($ ({2*sqrt(2)/2},0) $) node{$6$}
		($ ({4*sqrt(2)/2},0) $) node{$15$}
		($ ({6*sqrt(2)/2},0) $) node{$20$}
		($ ({8*sqrt(2)/2},0) $) node{$15$}
		($ ({10*sqrt(2)/2},0) $) node{$6$};
	}
\end{scope}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \alt<2->{(a+b)^{\textcolor{CUDRed}{4}}}{(a+b)^4} \)を
	計算しなさい}
\pause
\begin{tikzpicture}[rotate=0,scale=1,line width=2pt]
\draw[line width=16pt,CUDPink,line cap=round]
	($ ({2*sqrt(2)/2},{2*sqrt(2)/2}) $)--($ (13,{2*sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small
			\((\kern1.3em)^{\textcolor{CUDRed}{4}}\)に対応};
\draw[line width=16pt,CUDBrightGreen!75,line cap=round]
	($ ({3*sqrt(2)/2},{3*sqrt(2)/2}) $)--($ (13,{3*sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small$(\kern1.3em)^3$に対応}
	($ ({sqrt(2)/2},{sqrt(2)/2}) $)--($ (13,{sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small$(\kern1.3em)^5$に対応};
\drawpascal
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( (\alt<2->{\textcolor{CUDRed}{a}
	+\textcolor{CUDGreen}{b}}{a+b})^4 \)を計算しなさい}
\begin{tikzpicture}[scale=2.4, line width=2pt, anchor=base, >=stealth]
\coordinate (A) at (0,3);
\coordinate (B) at (1,3);
\coordinate (C) at (2,3);
\coordinate (D) at (3,3);
\coordinate (E) at (4,3);
\coordinate (F) at (5,3);

\draw(A) node{\( 1 \)}
	++(1,0) node{\( 4 \)}
	++(1,0) node{\( 6 \)}
	++(1,0) node{\( 4 \)}
	++(1,0) node{\( 1 \)};

\visible<2>{\begin{scope}
	\footnotesize
	\fill[CUDBrightCyan](-0.2,1.7) rectangle ++(0.4,0.4)
		(3.8,2.3) rectangle ++(0.4,0.4);
	\foreach \x in {1,2,3,4}{
		\draw[->,CUDRed](4.9-\x,2.7) to[out=150,in=30]
			node[midway,fill=white,inner sep=0pt]
				{\(\times a\)}++(-0.8,0);
		\draw[->,CUDGreen](\x-0.9,1.7) to[out=-30,in=-150]
			node[midway,fill=white,inner sep=0pt,yshift=-1ex]
			{\(\times b\)}++(0.8,0);
		}
	\end{scope}
	}

\visible<2->{\draw(A)++(0,-0.6) node{\( a^4 \)}
		++(1,0) node{\( a^3 \)}
		++(1,0) node{\( a^2 \)}
		++(1,0) node{\( a \)}
		++(1,0) node{\( 1 \)};
	\draw(A)++(0,-1.2) node{\( 1 \)}
		++(1,0) node{\( b \)}
		++(1,0) node{\( b^2 \)}
		++(1,0) node{\( b^3 \)}
		++(1,0) node{\( b^4 \)};
	}

\visible<3->{\foreach \i in {A,...,E}{\drawarrow}
	\draw(A)++(0,-2) node{\( a^4 \)}
		++(0.9,0) node{\( {}+4a^3 b \)}
		++(1.1,0) node{\( {}+6a^2 b^2 \)}
		++(1,0) node{\( {}+4a b^3 \)}
		++(1,0) node{\( {}+b^4 \)}
		++(1,0) node{\□答};
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \alt<2->{(x+2)^{\textcolor{CUDRed}{3}}}{(x+2)^3} \)を
	計算しなさい}
\pause
\begin{tikzpicture}[rotate=0,scale=1,line width=2pt]
\draw[line width=16pt,CUDPink,line cap=round]
	($ ({3*sqrt(2)/2},{3*sqrt(2)/2}) $)--($ (13,{3*sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small
		\((\kern1.3em)^{\textcolor{CUDRed}{3}}\)に対応};
\draw[line width=16pt,CUDBrightGreen!75,line cap=round]
	($ ({2*sqrt(2)/2},{2*sqrt(2)/2}) $)--($ (13,{2*sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small$(\kern1.3em)^4$に対応}
	($ ({sqrt(2)/2},{sqrt(2)/2}) $)--($ (13,{sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small$(\kern1.3em)^5$に対応};
\drawpascal
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( (\alt<2->{\textcolor{CUDRed}{x}
	+\textcolor{CUDGreen}{2}}{x+2} )^3
	\)を計算しなさい}
\begin{tikzpicture}[scale=2.4,line width=2pt, anchor=base, >=stealth]
\coordinate (A) at (0,3);
\coordinate (B) at (1,3);
\coordinate (C) at (2,3);
\coordinate (D) at (3,3);
\coordinate (E) at (4,3);
\coordinate (F) at (5,3);

\draw(A) node{\( 1 \)}
	++(1,0) node{\( 3 \)}
	++(1,0) node{\( 3 \)}
	++(1,0) node{\( 1 \)};
\visible<2>{\begin{scope}
	\footnotesize
	\fill[CUDBrightCyan](-0.2,1.7) rectangle ++(0.4,0.4)
		(2.8,2.3) rectangle ++(0.4,0.4);
	\foreach \x in {1,2,3}{
		\draw[->,CUDRed](3.9-\x,2.7) to[out=150,in=30]
			node[fill=white,inner sep=0pt]
				{\(\times x\)}++(-0.8,0);
		\draw[->,CUDGreen](\x-0.9,1.7) to[out=-30,in=-150]
			node[fill=white,inner sep=0pt,yshift=-1ex]
			{\(\times2\)}++(0.8,0);
		}
	\end{scope}
	}

\visible<2->{\draw(A)++(0,-0.6) node{\( x^3 \)}
	++(1,0) node{\( x^2 \)}
	++(1,0) node{\( x \)}
	++(1,0) node{\( 1 \)};
	\draw(A)++(0,-1.2) node{\( 1 \)}
		++(1,0) node{\( 2 \)}
		++(1,0) node{\( 4 \)}
		++(1,0) node{\( 8 \)};
	}
\visible<3->{\foreach \i in {A,...,D}{\drawarrow}
	\draw(A)++(0,-2) node{\( x^3 \)}
	++(1,0) node{\( {}+6x^2 \)}
	++(1,0) node{\( {}+12x \)}
	++(1,0) node{\( {}+8 \)}
	++(1,0) node{\□答};
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \alt<2->{(x+2)^{\textcolor{CUDRed}{4}}}{(x+2)^4} \)を
	計算しなさい}
\pause
\begin{tikzpicture}[rotate=0,scale=1,line width=2pt]
\draw[line width=16pt,CUDPink,line cap=round]
	($ ({2*sqrt(2)/2},{2*sqrt(2)/2}) $)--($ (13,{2*sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small
			\((\kern1.3em)^{\textcolor{CUDRed}{4}}\)に対応};
\draw[line width=16pt,CUDBrightGreen!75,line cap=round]
	($ ({3*sqrt(2)/2},{3*sqrt(2)/2}) $)--($ (13,{3*sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small$(\kern1.3em)^3$に対応}
	($ ({sqrt(2)/2},{sqrt(2)/2}) $)--($ (13,{sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small$(\kern1.3em)^5$に対応};
\drawpascal
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( (\alt<2->{\textcolor{CUDRed}{x}
	+\textcolor{CUDGreen}{2}}{x+2})^4 \)を計算しなさい}
\begin{tikzpicture}[scale=2.4, line width=2pt, anchor=base, >=stealth]
\coordinate (A) at (0,3);
\coordinate (B) at (1,3);
\coordinate (C) at (2,3);
\coordinate (D) at (3,3);
\coordinate (E) at (4,3);
\coordinate (F) at (5,3);

\draw(A) node{\( 1 \)}
	++(1,0) node{\( 4 \)}
	++(1,0) node{\( 6 \)}
	++(1,0) node{\( 4 \)}
	++(1,0) node{\( 1 \)};
\visible<2>{\begin{scope}
	\footnotesize
	\fill[CUDBrightCyan](-0.2,1.7) rectangle ++(0.4,0.4)
		(3.8,2.3) rectangle ++(0.4,0.4);
	\foreach \x in {1,2,3,4}{
		\draw[->,CUDRed](4.9-\x,2.7) to[out=150,in=30]
			node[midway,fill=white,inner sep=0pt]
				{\(\times x\)}++(-0.8,0);
		\draw[->,CUDGreen](\x-0.9,1.7) to[out=-30,in=-150]
			node[midway,fill=white,inner sep=0pt,yshift=-1ex]
			{\(\times2\)}++(0.8,0);
		}
	\end{scope}
	}

\visible<2->{\draw(A)++(0,-0.6) node{\( x^4 \)}
		++(1,0) node{\( x^3 \)}
		++(1,0) node{\( x^2 \)}
		++(1,0) node{\( x \)}
		++(1,0) node{\( 1 \)}
		(A)++(0,-1.2) node{\( 1 \)}
		++(1,0) node{\( 2 \)}
		++(1,0) node{\( 4 \)}
		++(1,0) node{\( 8 \)}
		++(1,0) node{\( 16 \)};
	}

\visible<3->{\foreach \i in {A,...,E}{\drawarrow}
	\draw(A)++(0,-2) node{\( x^4 \)}
		++(1,0) node{\( {}+8x^3 \)}
		++(1,0) node{\( {}+24x^2 \)}
		++(1,0) node{\( {}+32x \)}
		++(1,0) node{\( {}+16 \)}
		++(1,0) node{\□答};
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{{\rm C}を使って\( \alt<3->{(\textcolor{CUDRed}{x}
	+\textcolor{CUDGreen}{2})}{(x+2)}^4 \)の計算は分かりにくいかも}
\begin{tikzpicture}[scale=2.4, line width=2pt, anchor=base, >=stealth]
\coordinate (A) at (0,3);
\coordinate (B) at (1,3);
\coordinate (C) at (2,3);
\coordinate (D) at (3,3);
\coordinate (E) at (4,3);
\coordinate (F) at (5,3);

\visible<2-3>{\draw(A) node{\( {}_4{\rm C}_0 \)}
		++(1,0) node{\( {}_4{\rm C}_1 \)}
		++(1,0) node{\( {}_4{\rm C}_2 \)}
		++(1,0) node{\( {}_4{\rm C}_3 \)}
		++(1,0) node{\( {}_4{\rm C}_4 \)};
	}

\visible<3>{\begin{scope}
	\footnotesize
	\fill[CUDBrightCyan](-0.2,1.7) rectangle ++(0.4,0.4)
		(3.8,2.3) rectangle ++(0.4,0.4);
	\foreach \x in {1,2,3,4}{
		\draw[->,CUDRed](4.9-\x,2.7) to[out=150,in=30]
			node[midway,fill=white,inner sep=0pt]
				{\(\times x\)}++(-0.8,0);
		\draw[->,CUDGreen](\x-0.9,1.7) to[out=-30,in=-150]
			node[midway,fill=white,inner sep=0pt,yshift=-1ex]
			{\(\times2\)}++(0.8,0);
		}
	\end{scope}
	}

\visible<3->{\draw(A)++(0,-0.6) node{\( x^4 \)}
		++(1,0) node{\( x^3 \)}
		++(1,0) node{\( x^2 \)}
		++(1,0) node{\( x \)}
		++(1,0) node{\( 1 \)}
		(A)++(0,-1.2) node{\( 1 \)}
		++(1,0) node{\( 2 \)}
		++(1,0) node{\( 4 \)}
		++(1,0) node{\( 8 \)}
		++(1,0) node{\( 16 \)};
	}

\visible<4>{\draw(A) node{\( 1 \)};
	\draw(B) node{\( \tfrac{\,4\,}{1} \)};
	\draw(C) node{\( \tfrac{\,4\!\times\!3\,}{2\!\times\!1} \)};
	\draw(D) node{\( \tfrac{\,4\!\times\!3\!\times\!2\,}
				{3\!\times\!2\!\times\!1} \)};
	\draw(E) node{\( \tfrac{\,4\!\times\!3\!\times\!2\!\times\!1\,}
				{4\!\times\!3\!\times\!2\!\times\!1} \)};
	}
\visible<5->{\draw(A) node{\( 1 \)}
		++(1,0) node{\( 4 \)}
		++(1,0) node{\( 6 \)}
		++(1,0) node{\( 4 \)}
		++(1,0) node{\( 1 \)};
	}
\visible<6->{\foreach \i in {A,...,E}{\drawarrow}
	\draw(A)++(0,-2) node{\( x^4 \)}
		++(1,0) node{\( {}+8x^3 \)}
		++(1,0) node{\( {}+24x^2 \)}
		++(1,0) node{\( {}+32x \)}
		++(1,0) node{\( {}+16 \)}
		++(1,0) node{\□答};
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \alt<2->{(2x+1)^{\textcolor{CUDRed}{5}}}{(2x+1)^5} \)を
	計算しなさい}
\pause
\begin{tikzpicture}[rotate=0,scale=1,line width=2pt]
\draw[line width=16pt,CUDPink,line cap=round]
	($ ({sqrt(2)/2},{sqrt(2)/2}) $)--($ (13,{sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small
		\((\kern1.3em)^{\textcolor{CUDRed}{5}}\)に対応};
\draw[line width=16pt,CUDBrightGreen!75,line cap=round]
	($ ({3*sqrt(2)/2},{3*sqrt(2)/2}) $)--($ (13,{3*sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small$(\kern1.3em)^3$に対応}
	($ ({2*sqrt(2)/2},{2*sqrt(2)/2}) $)--($ (13,{2*sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small$(\kern1.3em)^4$に対応};
\drawpascal
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( (\alt<2->{\textcolor{CUDRed}{2x}
	+\textcolor{CUDGreen}{1}}{2x+1})^5 \)を計算しなさい}
\begin{tikzpicture}[scale=2.4, line width=2pt, anchor=base, >=stealth]
\coordinate (A) at (0,3);
\coordinate (B) at (1,3);
\coordinate (C) at (2,3);
\coordinate (D) at (3,3);
\coordinate (E) at (4,3);
\coordinate (F) at (5,3);

\visible<3->{\foreach \i in {A,...,F}{\drawarrow}}

\draw(A) node{\( 1 \)}
	++(1,0) node{\( 5 \)}
	++(1,0) node{\( 10 \)}
	++(1,0) node{\( 10 \)}
	++(1,0) node{\( 5 \)}
	++(1,0) node{\( 1 \)};
\visible<2>{\begin{scope}
		\footnotesize
		\fill[CUDBrightCyan](-0.2,1.7) rectangle ++(0.4,0.4)
			(4.8,2.3) rectangle ++(0.4,0.4);
		\foreach \x in {1,2,3,4,5}{
			\draw[->,CUDRed](5.9-\x,2.7) to[out=150,in=30]
				node[midway,fill=white,inner sep=0pt,yshift=1ex]
					{\(\times 2x\)}++(-0.8,0);
			\draw[->,CUDGreen](\x-0.9,1.7) to[out=-30,in=-150]
				node[midway,fill=white,inner sep=0pt,yshift=-2ex]
				{\(\times1\)}++(0.8,0);
			}
	\end{scope}
	}
\visible<2->{\draw(A)++(0,-0.6) node{\( 32x^5 \)}
			++(1,0) node{\( 16x^4 \)}
			++(1,0) node{\( 8x^3 \)}
			++(1,0) node{\( 4x^2 \)}
			++(1,0) node{\( 2x \)}
			++(1,0) node{\( 1 \)};
		\foreach \x in {A,...,F}\draw(\x)++(0,-1.2) node{\( 1 \)};
	}
\visible<3->{\draw(A)++(0,-2) node{\( 32x^5 \)}
		++(1,0) node{\( {}+80x^4 \)}
		++(1,0) node{\( {}+80x^3 \)}
		++(1,0) node{\( {}+40x^2 \)}
		++(1,0) node{\( {}+10x \)}
		++(1,0) node{\( {}+1 \)}
		++(0.6,0) node{\□答};
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( (2x-3y)^5 \)を計算しなさい}

\[ (2x-3y)^5=\Bigl(2x+(-3y)\Bigr)^5 \]

\centerline{と考えるとよい}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( (2x-3y)^{\textcolor{CUDRed}{5}} \)を計算しなさい}
\begin{tikzpicture}[rotate=0,scale=1,line width=2pt]
\draw[line width=16pt,CUDBrightGreen!75,line cap=round]
	($ ({3*sqrt(2)/2},{3*sqrt(2)/2}) $)--($ (13,{3*sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small$(\kern1.3em)^3$に対応}
	($ ({2*sqrt(2)/2},{2*sqrt(2)/2}) $)--($ (13,{2*sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small$(\kern1.3em)^4$に対応};
\draw[line width=16pt,CUDPink,line cap=round]
	($ ({sqrt(2)/2},{sqrt(2)/2}) $)--($ (13,{sqrt(2)/2}) $)
		node[black,xshift=-2em]{\small
		\((\kern1.3em)^{\textcolor{CUDRed}{5}}\)に対応};
\drawpascal
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \bigl(\alt<2>{\textcolor{CUDRed}{2x}
	+\textcolor{CUDGreen}{(-3y)}}{2x+(-3y)}\bigr)^5 \)を計算しなさい}
\begin{tikzpicture}[scale=2.4, line width=2pt,anchor=base, >=stealth]
\coordinate (A) at (0,3);
\coordinate (B) at (1,3);
\coordinate (C) at (2,3);
\coordinate (D) at (3,3);
\coordinate (E) at (4,3);
\coordinate (F) at (5,3);

\visible<3->{\foreach \i in {A,...,F}{\drawarrow}}
\draw(A) node{\( 1 \)}
	++(1,0) node{\( 5 \)}
	++(1,0) node{\( 10 \)}
	++(1,0) node{\( 10 \)}
	++(1,0) node{\( 5 \)}
	++(1,0) node{\( 1 \)};

\visible<2>{\begin{scope}
	\footnotesize
	\fill[CUDBrightCyan](-0.15,1.75) rectangle ++(0.3,0.3)
		(4.85,2.35) rectangle ++(0.3,0.3);
	\foreach \x in {1,...,5}{
		\draw[->,CUDRed](5.9-\x,2.7) to[out=150,in=30]
			node[midway,fill=white,inner sep=0pt,yshift=1ex]
				{\(\times 2x\)}++(-0.8,0);
		\draw[->,CUDGreen](\x-0.9,1.7) to[out=-30,in=-150]
			node[midway,fill=white,inner sep=0pt,yshift=-2ex]
			{\(\times(-3y)\)}++(0.8,0);
		}
	\end{scope}
	}
\small
\visible<2->{\draw(A)++(0,-0.6) node{\( 32x^5 \)}
		++(1,0) node{\( 16x^4 \)}
		++(1,0) node{\( 8x^3 \)}
		++(1,0) node{\( 4x^2 \)}
		++(1,0) node{\( 2x \)}
		++(1,0) node{\( 1 \)}

		(A)++(0,-1.2) node{\( 1 \)}
		++(1,0) node{\( -3y \)}
		++(1,0) node{\( 9y^2 \)}
		++(1,0) node{\( -27y^3 \)}
		++(1,0) node{\( 81y^4 \)}
		++(1,0) node{\( -243y^5 \)};
	}
\footnotesize
\visible<3->{\draw(A)++(0,-2) node{\( 32x^5 \)}
		++(1,0) node{\( -240x^4y \)}
		++(1,0) node{\( +720x^3y^2 \)}
		++(1,0) node{\( -1080x^2y^3 \)}
		++(1,0) node{\( +810xy^4 \)}
		++(1,0) node{\( -243y^5 \)}
		++(0.6,0) node{\small\□答};
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{二項定理の重要度は低いのでは？}
定期考査で出題されるくらいで、二項定理そのものが入試に出題されることは
考えにくい。

%\bigskip
%\hskip-1zw
%（解く過程で二項定理を使う場合はあるかもしれないが…）

\bigskip
%マスターする必要性は低いと思うよ。
ある程度、解けるくらいでいいんじゃないかな。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




\end{document}




