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%   \\
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%%
%% �������@�������當�����͂��܂�܂��@������
%%
%% white �� black�@�̒u������������Ɩ͔͉𓚗p�����ł��܂��B
%%
%%
\begin{document}
\twocolumn[%
  \begin{center}
    \Large\bf $3$�N~���̌v�Z
  \end{center}
  \begin{flushright}
    \underline{\hspace{1cm}}�N\underline{\hspace{1cm}}�g\underline{\hspace{1cm}}��
    \hspace{1zw}����\underline{\hspace{5cm}}
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 \vspace{5mm}]

\parindent = 0zw 
%%������}
%���ӁD�𓚂͂��ׂĉ𓚗p���ɋL�����Ȃ����B

\begin{enumerate}

%\item ���̕��@�̓G���g�X�e�l�X��⿂ɂ��ďq�ׂ����̂ł���B
%���̕��@��p����$1$�`$50$�܂ł̑f���̌������߂Ȃ����B
%���̐��̕\��K���g�p���Ȃ����B
%
%\begin{tabular}{cccccccccc}
%\multicolumn{10}{l}{\ajMaru{1}$\>1$�������B}\\
%\multicolumn{10}{l}{\ajMaru{2}$\>2$���c����$2$�̔{�������ׂď����B}\\
%\multicolumn{10}{l}{\ajMaru{3}$\>3$���c����$3$�̔{�������ׂď����B}\\
%\multicolumn{10}{l}{�ȉ����̎菇���J��Ԃ��B}\\
%$1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & $9$ & $10$ \\
%$11$ & $12$ & $13$ & $14$ & $15$ & $16$ & $17$ & $18$ & $19$ & $20$ \\
%$21$ & $22$ & $23$ & $24$ & $25$ & $26$ & $27$ & $28$ & $29$ & $30$ \\
%$31$ & $32$ & $33$ & $34$ & $35$ & $36$ & $37$ & $38$ & $39$ & $40$ \\
%$41$ & $42$ & $43$ & $44$ & $45$ & $46$ & $47$ & $48$ & $49$ & $50$ \\
%\end{tabular}
%
%\LINE
\item \fbox{�@�@�@} �ɂ��Ă͂܂錾�t�������Ȃ����B

\begin{enumerate}

\item �� $2a^2+4ab$ �ɂ�����$2a$�� \fbox{�@\ajMaru{1}�@} �Ƃ����B

\item 
\begin{tabular}{@{}c@{}c@{}c@{}}
& \fbox{�@\ajMaru{2}�@} & \\[-6pt]
& \,$\longrightarrow$\, &\\[-12pt]
$x^2+3x+2$ & & $(x+1)(x+2)$ \\[-12pt]
& $\longleftarrow$ &\\[-4pt]
\fbox{~\ajMaru{3}~}�̌` & \fbox{�@\ajMaru{4}�@} & \fbox{~\ajMaru{5}~}�̌` \\
\end{tabular}

���̂Ƃ�$x\!+\!1$�𑽍���$x^2\!+\!3x\!+\!2$��\,\fbox{�@\ajMaru{6}�@}\,�Ƃ���\!�B
%\item �f���Ƃ�$1$�Ƃ��̐����g�̂ق���\fbox{�@\ajMaru{1}�@}���Ȃ����R���ł��B
%$1$����$20$�܂ł̊Ԃɑf����\fbox{�@\ajMaru{2}�@}����܂��B

%\item ���R�����������̐����̐ς̌`�ŕ\�����Ƃ��C
%����$1$��$1$�̐��������Ƃ̎��R����\fbox{�@\ajMaru{3}�@}�Ƃ����B
%�Ⴆ��$6$��\fbox{�@\ajMaru{3}�@}��\fbox{�@\ajMaru{4}�@}�ł��B

%\item �f���ł��������\fbox{�@\ajMaru{3}�@}�Ƃ����܂��B
%�Ⴆ��$6$��\fbox{�@\ajMaru{3}�@}��\fbox{�@\ajMaru{4}�@}�ł��B
%
%\item ���R����\fbox{�@\ajMaru{4}�@}�����̐ςŕ\�����Ƃ��C���̐���f������������Ƃ����܂��B
%�Ⴆ��$6$��f�������������\fbox{�@\ajMaru{6}�@}�ƂȂ�܂��B
\end{enumerate}

\begin{tabular}{|@{\vrule width 0.4pt}c@{}|c|@{}c@{}|c|@{\vrule width 0.4pt}}
\noalign{\hrule height 0.4pt}\hline
& \hspace{33mm} & & \hspace{33mm} \\[-8pt]
~\ajMaru{1}~ & \color{white}{���ʂȈ���} & ~\ajMaru{2}~ & \color{white}{��������} \\[-8pt]
& & & \\
\hline
& & & \\[-8pt]
~\ajMaru{3}~ & {\color{white}{(�P������)�a}} & ~\ajMaru{4}~ & \color{white}{�W�J} \\[-8pt]
& & & \\
\hline
& & & \\[-8pt]
~\ajMaru{5}~ & {\color{white}{(������)��}} & ~\ajMaru{6}~ & \color{white}{����} \\[-8pt]
& & & \\
\noalign{\hrule height 0.4pt}\hline
\end{tabular}

\vspace{1mm}
\item ���̌v�Z�����Ȃ����B
\begin{enumerate}
\item $-6x\times (x-2y)$

\vfill
\LINEK{-6x^2+12xy}

\item $(6a^2+9a)\div 3a$

\vfill
\LINEK{2a+3}
\end{enumerate}

\vspace{1mm}
\item ���̎���W�J���Ȃ����B
\begin{enumerate}

\item $(x-3)(y+5)$
\vfill
\LINEK{xy+5x-3y-15}

\item $(x-2)(x+4)$
\vfill
\LINEK{x^2+2x-8}

\item $(3x+5)^2$
\vfill
\LINEK{9x^2+30x+25}

\item $(a+6)(a-6)$
\vfill
\LINEK{a^2-36}

\item $(2x-1)(2x+7)$
\vfill
\LINEK{4x^2+12x-7}

\item $(2x-1)^2-3(x+1)(x-5)$
\vfill
%4x^2-4x+1-3x^2+12x+15
\LINEK{x^2+8x+16}

\end{enumerate}

\item ���̎��������������Ȃ����B
\begin{enumerate}

\item $3ab^2-6ab$
\vfill
\LINEK{3ab(b-2)}

\item $x^2+5x+6$
\vfill
\LINEK{(x+2)(x+3)}

\item $9x^2-24x+16$
\vfill
\LINEK{(3x-4)^2}

\item $(x-y)^2+4(x-y)+3$
\vfill
\LINEK{(x-y+1)(x-y+3)}

\item $3x(2-y)-y+2$
\vfill
\LINEK{(3x+1)(2-y)}

\newpage

\item $a^2+6ab+9b^2-1$
\vfill
\LINEK{(a+3b+1)(a+3b-1)}

\item $3x^2+9x-54$
\vfill
\LINEK{3(x+6)(x-3)}

\end{enumerate}

\vspace{1mm}
\item ���̎��̒l�����߂Ȃ����B

\begin{enumerate}
\item $x=198$�̂Ƃ��C$x^2+4x+4$�̒l

\vfill
\LINEK{40000}

\item $x=3.75,\,y=2.25$�̂Ƃ��C$x^2-y^2$�̒l

\vfill
\LINEK{9}

\end{enumerate}

\item ���̐���f�����������Ȃ����B

\begin{enumerate}
\begin{minipage}{11zw}
\item $84$

\vspace{12mm}
\begin{tabular}{|@{\vrule width 0.4pt}l|@{\vrule width 0.4pt}}
\noalign{\hrule height 0.4pt}\hline
\hspace{30mm} \\[-12pt]
\multicolumn{1}{c}{\color{white}{$84=2^2\times 3\times 7$}} \\[-12pt]
\\
\noalign{\hrule height 0.4pt}\hline
\end{tabular}
\end{minipage}
\begin{minipage}{11zw}
\item $120$

\vspace{12mm}
\begin{tabular}{|@{\vrule width 0.4pt}l|@{\vrule width 0.4pt}}
\noalign{\hrule height 0.4pt}\hline
\hspace{30mm} \\[-12pt]
\multicolumn{1}{c}{\color{white}{$120=2^3\times 3\times 5$}}\\[-12pt]
\\
\noalign{\hrule height 0.4pt}\hline
\end{tabular}
\end{minipage}
\end{enumerate}

\vspace{1mm}
\item $3$�A�������̕����a��$1$���������$3$�̔{���ɂȂ�܂��B���̂��Ƃ𕶎����g���ďؖ����Ȃ����B

(��D$2^2+3^2+4^2+1=30$)

\vspace{1mm}
\hspace{-4mm}
\begin{tabular}{|@{\vrule width 0.4pt}l@{}|@{\vrule width 0.4pt}}
\noalign{\hrule height 0.4pt}\hline
~��������\\
\hspace{1zw}\color{white}{$n$�𐮐��Ƃ���$3$�A��������$n-1$\,,\,$n$\,,\,$n+1$�Ƃ���B}\\
\hspace{1zw}\color{white}{$~~~(n-1)^2+n^2+(n+1)^2+1$} \\
\hspace{1zw}\color{white}{$=n^2-2n+1+n^2+n^2+2n+1+1$} \\
\hspace{1zw}\color{white}{$=3n^2+3$} \\
\hspace{1zw}\color{white}{$=3(n^2+1)$} \\
\hspace{1zw}\color{white}{$n$�͐������$n^2+1$�͐����B} \\
\hspace{1zw}\color{white}{�����$3$�A�������̕����a��$1$���������$3$�̔{���ɂȂ�B} \\
\\
\hspace{85mm} \\
\noalign{\hrule height 0.4pt}\hline
\end{tabular}

\vspace{3mm}
\item ~

\vspace{-1.5zw}
\begin{minipage}{18zw}
�E�̐}�͈�ӂ�$1$\ajLig{cm}�̗����̂�$27$�ςݏグ�Ĉ�ӂ�$3$\ajLig{cm}�̗����̂�������}�ł��B�ȉ��̖₢�ɓ����Ȃ����B
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\begin{enumerate}
\item ��x�Ɍ��邱�Ƃ̂ł��闧���͍̂ő剽�ł����B

\LINEK{19}

\item ��ӂ�$1$\ajLig{cm}�̗����̂�$n^3$�g���Ĉ�ӂ�$n$\ajLig{cm}�̗����̂�������Ƃ��C��x�Ɍ��邱�Ƃ̂ł��闧���͍̂ő剽�ł����B$n$���g���ĕ\���Ȃ����B

{\color{white}{$n^2+n(n-1)+(n-1)^2$}}

\LINEK{3n^2-3n+1}

\end{enumerate}
\end{enumerate}

\end{document}
