次の式を展開しよう。
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\SLA{x} \def\SLF{+} \def\SLB{2y} \def\SRA{x} \def\SRF{} \def\SRB{-3y} \def\SLRA{x^2} \def\SLRB{-6y^2} \def\SLARB{-3xy} \def\SLBRA{2xy} \def\SM{-xy} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}{\scriptsize #2}\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{red}{\fbox{Point}} & \ \colMM{red}{慣れるまでは余白にメモしよう!}\\ \\ & \colMM{orange}{\bf 左} \colMM{magenta}{\bf 右} \colMM{green}{\bf 左} \colMM{deepskyblue}{\bf 右}\\ & (\colBX{bisque}{$\SLA$}\SLF\colBX{violet}{$\SLB$})(\colBX{palegreen}{$\SRA$}\SRF\colBX{lightcyan}{$\SRB$})\\ & \colMM{orange}{\bf 外} \colMM{magenta}{\bf 中} \colMM{green}{\bf 中} \colMM{deepskyblue}{\bf 外}\\ \\ ・ & \colBX{bisque}{左} \times \colBX{palegreen}{左} = (\colBX{bisque}{$\SLA$}) \times (\colBX{palegreen}{$\SRA$}) = \colFR{red}{$\SLRA$}\\ ・ & \colBX{violet}{右} \times \colBX{lightcyan}{右} = (\colBX{violet}{$\SLB$}) \times (\colBX{lightcyan}{$\SRB$}) = \colFR{blue}{$\SLRB$}\\ \\ ・ & \colBX{bisque}{外} \times \colBX{lightcyan}{外} = (\colBX{bisque}{$\SLA$}) \times (\colBX{lightcyan}{$\SRB$}) = \SLARB\\ ・ & \colBX{violet}{中} \times \colBX{palegreen}{中} = (\colBX{violet}{$\SLB$}) \times (\colBX{palegreen}{$\SRA$}) = \SLBRA\\\hline & \colMM{red}{ 足して} \colBX{yellow}{$\SM$} \\ \\ \colMM{red}{\fbox{Answer}} &\\ & (\SLA\SLF\SLB)(\SRA\SRF\SRB) = \colFR{red}{$\SLRA$}\,\colBX{yellow}{$\SM$}\,\colFR{blue}{$\SLRB$} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\SLA{x} \def\SLF{} \def\SLB{-4y} \def\SRA{x} \def\SRF{+} \def\SRB{2y} \def\SLRA{x^2} \def\SLRB{-8y^2} \def\SLARB{2xy} \def\SLBRA{-4xy} \def\SM{-2xy} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}{\scriptsize #2}\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{red}{\fbox{Point}} & \ \colMM{red}{慣れるまでは余白にメモしよう!}\\ \\ & \colMM{orange}{\bf 左} \colMM{magenta}{\bf 右} \colMM{green}{\bf 左} \colMM{deepskyblue}{\bf 右}\\ & (\colBX{bisque}{$\SLA$}\SLF\colBX{violet}{$\SLB$})(\colBX{palegreen}{$\SRA$}\SRF\colBX{lightcyan}{$\SRB$})\\ & \colMM{orange}{\bf 外} \colMM{magenta}{\bf 中} \colMM{green}{\bf 中} \colMM{deepskyblue}{\bf 外}\\ \\ ・ & \colBX{bisque}{左} \times \colBX{palegreen}{左} = (\colBX{bisque}{$\SLA$}) \times (\colBX{palegreen}{$\SRA$}) = \colFR{red}{$\SLRA$}\\ ・ & \colBX{violet}{右} \times \colBX{lightcyan}{右} = (\colBX{violet}{$\SLB$}) \times (\colBX{lightcyan}{$\SRB$}) = \colFR{blue}{$\SLRB$}\\ \\ ・ & \colBX{bisque}{外} \times \colBX{lightcyan}{外} = (\colBX{bisque}{$\SLA$}) \times (\colBX{lightcyan}{$\SRB$}) = \SLARB\\ ・ & \colBX{violet}{中} \times \colBX{palegreen}{中} = (\colBX{violet}{$\SLB$}) \times (\colBX{palegreen}{$\SRA$}) = \SLBRA\\\hline & \colMM{red}{ 足して} \colBX{yellow}{$\SM$} \\ \\ \colMM{red}{\fbox{Answer}} &\\ & (\SLA\SLF\SLB)(\SRA\SRF\SRB) = \colFR{red}{$\SLRA$}\,\colBX{yellow}{$\SM$}\,\colFR{blue}{$\SLRB$} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\SLA{2x} \def\SLF{+} \def\SLB{3} \def\SRA{4x} \def\SRF{+} \def\SRB{5} \def\SLRA{8x^2} \def\SLRBF{+} \def\SLRB{15} \def\SLARB{10x} \def\SLBRA{12x} \def\SMF{+} \def\SM{22x} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}{\scriptsize #2}\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{red}{\fbox{Point}} & \ \colMM{red}{慣れるまでは余白にメモしよう!}\\ \\ & \colMM{orange}{\bf 左} \colMM{magenta}{\bf 右} \colMM{green}{\bf 左} \colMM{deepskyblue}{\bf 右}\\ & (\colBX{bisque}{$\SLA$}\SLF\colBX{violet}{$\SLB$})(\colBX{palegreen}{$\SRA$}\SRF\colBX{lightcyan}{$\SRB$})\\ & \colMM{orange}{\bf 外} \colMM{magenta}{\bf 中} \colMM{green}{\bf 中} \colMM{deepskyblue}{\bf 外}\\ \\ ・ & \colBX{bisque}{左} \times \colBX{palegreen}{左} = (\colBX{bisque}{$\SLA$}) \times (\colBX{palegreen}{$\SRA$}) = \colFR{red}{$\SLRA$}\\ ・ & \colBX{violet}{右} \times \colBX{lightcyan}{右} = (\colBX{violet}{$\SLB$}) \times (\colBX{lightcyan}{$\SRB$}) = \colFR{blue}{$\SLRB$}\\ \\ ・ & \colBX{bisque}{外} \times \colBX{lightcyan}{外} = (\colBX{bisque}{$\SLA$}) \times (\colBX{lightcyan}{$\SRB$}) = \SLARB\\ ・ & \colBX{violet}{中} \times \colBX{palegreen}{中} = (\colBX{violet}{$\SLB$}) \times (\colBX{palegreen}{$\SRA$}) = \SLBRA\\\hline & \colMM{red}{ 足して} \colBX{yellow}{$\SM$} \\ \\ \colMM{red}{\fbox{Answer}} &\\ & (\SLA\SLF\SLB)(\SRA\SRF\SRB) = \colFR{red}{$\SLRA$}\,\colBX{yellow}{$\SMF\SM$}\,\colFR{blue}{$\SLRBF\SLRB$} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\SLA{3x} \def\SLF{+} \def\SLB{1} \def\SRA{x} \def\SRF{+} \def\SRB{2} \def\SLRA{3x^2} \def\SLRBF{+} \def\SLRB{2} \def\SLARB{6x} \def\SLBRA{x} \def\SMF{+} \def\SM{7x} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}{\scriptsize #2}\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{red}{\fbox{Point}} & \ \colMM{red}{慣れるまでは余白にメモしよう!}\\ \\ & \colMM{orange}{\bf 左} \colMM{magenta}{\bf 右} \colMM{green}{\bf 左} \colMM{deepskyblue}{\bf 右}\\ & (\colBX{bisque}{$\SLA$}\SLF\colBX{violet}{$\SLB$})(\colBX{palegreen}{$\SRA$}\SRF\colBX{lightcyan}{$\SRB$})\\ & \colMM{orange}{\bf 外} \colMM{magenta}{\bf 中} \colMM{green}{\bf 中} \colMM{deepskyblue}{\bf 外}\\ \\ ・ & \colBX{bisque}{左} \times \colBX{palegreen}{左} = (\colBX{bisque}{$\SLA$}) \times (\colBX{palegreen}{$\SRA$}) = \colFR{red}{$\SLRA$}\\ ・ & \colBX{violet}{右} \times \colBX{lightcyan}{右} = (\colBX{violet}{$\SLB$}) \times (\colBX{lightcyan}{$\SRB$}) = \colFR{blue}{$\SLRB$}\\ \\ ・ & \colBX{bisque}{外} \times \colBX{lightcyan}{外} = (\colBX{bisque}{$\SLA$}) \times (\colBX{lightcyan}{$\SRB$}) = \SLARB\\ ・ & \colBX{violet}{中} \times \colBX{palegreen}{中} = (\colBX{violet}{$\SLB$}) \times (\colBX{palegreen}{$\SRA$}) = \SLBRA\\\hline & \colMM{red}{ 足して} \colBX{yellow}{$\SM$} \\ \\ \colMM{red}{\fbox{Answer}} &\\ & (\SLA\SLF\SLB)(\SRA\SRF\SRB) = \colFR{red}{$\SLRA$}\,\colBX{yellow}{$\SMF\SM$}\,\colFR{blue}{$\SLRBF\SLRB$} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\SLA{x} \def\SLF{+} \def\SLB{2} \def\SRA{x} \def\SRF{+} \def\SRB{7} \def\SLRA{x^2} \def\SLRBF{+} \def\SLRB{14} \def\SLARB{7x} \def\SLBRA{2x} \def\SMF{+} \def\SM{9x} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}{\scriptsize #2}\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{red}{\fbox{Point}} & \ \colMM{red}{慣れるまでは余白にメモしよう!}\\ \\ & \colMM{orange}{\bf 左} \colMM{magenta}{\bf 右} \colMM{green}{\bf 左} \colMM{deepskyblue}{\bf 右}\\ & (\colBX{bisque}{$\SLA$}\SLF\colBX{violet}{$\SLB$})(\colBX{palegreen}{$\SRA$}\SRF\colBX{lightcyan}{$\SRB$})\\ & \colMM{orange}{\bf 外} \colMM{magenta}{\bf 中} \colMM{green}{\bf 中} \colMM{deepskyblue}{\bf 外}\\ \\ ・ & \colBX{bisque}{左} \times \colBX{palegreen}{左} = (\colBX{bisque}{$\SLA$}) \times (\colBX{palegreen}{$\SRA$}) = \colFR{red}{$\SLRA$}\\ ・ & \colBX{violet}{右} \times \colBX{lightcyan}{右} = (\colBX{violet}{$\SLB$}) \times (\colBX{lightcyan}{$\SRB$}) = \colFR{blue}{$\SLRB$}\\ \\ ・ & \colBX{bisque}{外} \times \colBX{lightcyan}{外} = (\colBX{bisque}{$\SLA$}) \times (\colBX{lightcyan}{$\SRB$}) = \SLARB\\ ・ & \colBX{violet}{中} \times \colBX{palegreen}{中} = (\colBX{violet}{$\SLB$}) \times (\colBX{palegreen}{$\SRA$}) = \SLBRA\\\hline & \colMM{red}{ 足して} \colBX{yellow}{$\SM$} \\ \\ \colMM{red}{\fbox{Answer}} &\\ & (\SLA\SLF\SLB)(\SRA\SRF\SRB) = \colFR{red}{$\SLRA$}\,\colBX{yellow}{$\SMF\SM$}\,\colFR{blue}{$\SLRBF\SLRB$} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\SLA{2x} \def\SLF{+} \def\SLB{1} \def\SRA{x} \def\SRF{+} \def\SRB{2} \def\SLRA{2x^2} \def\SLRBF{+} \def\SLRB{2} \def\SLARB{4x} \def\SLBRA{x} \def\SMF{+} \def\SM{5x} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}{\scriptsize #2}\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colMM{red}{\fbox{Point}} & \ \colMM{red}{慣れるまでは余白にメモしよう!}\\ \\ & \colMM{orange}{\bf 左} \colMM{magenta}{\bf 右} \colMM{green}{\bf 左} \colMM{deepskyblue}{\bf 右}\\ & (\colBX{bisque}{$\SLA$}\SLF\colBX{violet}{$\SLB$})(\colBX{palegreen}{$\SRA$}\SRF\colBX{lightcyan}{$\SRB$})\\ & \colMM{orange}{\bf 外} \colMM{magenta}{\bf 中} \colMM{green}{\bf 中} \colMM{deepskyblue}{\bf 外}\\ \\ ・ & \colBX{bisque}{左} \times \colBX{palegreen}{左} = (\colBX{bisque}{$\SLA$}) \times (\colBX{palegreen}{$\SRA$}) = \colFR{red}{$\SLRA$}\\ ・ & \colBX{violet}{右} \times \colBX{lightcyan}{右} = (\colBX{violet}{$\SLB$}) \times (\colBX{lightcyan}{$\SRB$}) = \colFR{blue}{$\SLRB$}\\ \\ ・ & \colBX{bisque}{外} \times \colBX{lightcyan}{外} = (\colBX{bisque}{$\SLA$}) \times (\colBX{lightcyan}{$\SRB$}) = \SLARB\\ ・ & \colBX{violet}{中} \times \colBX{palegreen}{中} = (\colBX{violet}{$\SLB$}) \times (\colBX{palegreen}{$\SRA$}) = \SLBRA\\\hline & \colMM{red}{ 足して} \colBX{yellow}{$\SM$} \\ \\ \colMM{red}{\fbox{Answer}} &\\ & (\SLA\SLF\SLB)(\SRA\SRF\SRB) = \colFR{red}{$\SLRA$}\,\colBX{yellow}{$\SMF\SM$}\,\colFR{blue}{$\SLRBF\SLRB$} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
レベルG
次の計算をせよ。
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\newcommand\colNS[2]{\textcolor{#1}{#2}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}} \begin{align*} & (3x+1)(x-2)-x(2-x)\\ &= 3x(x-2)+1(x-2)-x(2-x)\\ &= 3x^2-6x+x-2-2x+x^2\\ &= 4x^2-7x-2 \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
【別解】
\newcommand\colNS[2]{\textcolor{#1}{#2}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}} \begin{align*} & (3x+1)(x-2)-x(2-x)\\ &= (3x+1)(x-2)+x(x-2)\\ &= (3x+1+x)(x-2)\\ &= (4x+1)(x-2)\\ &= 4x(x-2)+1(x-2)\\ &= 4x^2-8x+x-2\\ &= 4x^2-7x-2 \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\newcommand\colNS[2]{\textcolor{#1}{#2}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}} \begin{align*} & (3a-1)(a+2)-5a(a+2)\\ &= 3a(a+2)-1(a+2)-5a(a+2)\\ &= 3a^2+6a-a-2-5a^2-10a\\ &= -2a^2-5a-2 \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
【別解】
\newcommand\colNS[2]{\textcolor{#1}{#2}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}} \begin{align*} & (3a-1)(a+2)-5a(a+2)\\ &= (3a-1-5a)(a+2)\\ &= (-2a-1)(a+2)\\ &= -2a(a+2)-1(a+2)\\ &= -2a^2-4a-a-2\\ &= -2a^2-5a-2 \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan