次の式を因数分解しよう。
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【解答】次数引き分け➡xで整理
\def\S{2x^2+xy-y^2+4x+y+2} \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*} & \S\\ & \colMM{red}{ \Darr x\ (の個数)で整理!}\\ &= 2x^2+(xy+4x)+(-y^2+y+2)\\ & \colMM{orange}{ ①共通\Darr }\colMM{green}{ \Darr ①マイナスを外へ}\\ &= 2x^2+(y+4)x-(y^2-y-2)\\ & \colMM{green}{ \Darr ②たすきがけ}\\ &= 2x^2+(y+4)x-(y+1)(y-2)\colMM{red}{\Leftarrow x\ の2次式!}\\ & \colMM{red}{ \Darr ②たすきがけ※}\\ &= \left\{x+(y+1)\right\}\left\{2x-(y-2)\right\}\\ \\ &= (x+y+1)(2x-y+2)\\ \\ \end{align*}\\ \\ \def\MA{2x^2} \def\MBF{+} \def\MB{(y+4)x} \def\MCF{} \def\MC{-(y+1)(y-2)} \def\SLA{x} \def\SLF{+} \def\SLB{(y+1)} \def\SRA{2x} \def\SRF{} \def\SRB{-(y-2)} \def\SRALB{(2y+2)x} \def\SLARB{(-y+2)x} \begin{align*} \colMM{red}{\fbox{②たすきがけ※} } & \end{align*} \\ \begin{alignedat}{3} \colBX{bisque}{$\SLA$} & & \colBX{palegreen}{$\SLB$} && \colBX{palegreen}{$\SRALB$}\\ \colBX{palegreen}{$\SRA$} & & \colBX{bisque}{$\SRB$} && \colBX{bisque}{$\SLARB$}\\\hline \MA & & \MC && \MB\\ \colMM{red}{\bf 先頭} & & \colMM{red}{\bf 最後} && \colMM{red}{\bf 真ん中} \end{alignedat}\\ %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
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【解答】次数引き分け➡xで整理
\def\S{x^2+3xy+2y^2-x-3y-2} \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*} & \S\\ & \colMM{red}{ \Darr x\ (の個数)で整理!}\\ &= x^2+(3xy-x)+(2y^2-3y-2)\\ & \colMM{orange}{ ①共通\Darr }\colMM{green}{ \Darr ②たすきがけ}\\ &= x^2+(3y-1)x+(y-2)(2y+1)\colMM{red}{\Leftarrow x\ の2次式!}\\ & \colMM{red}{ \Darr ②たすきがけ※}\\ &= \left\{x+(y-2)\right\}\left\{x+(2y+1)\right\}\\ \\ &= (x+y-2)(x+2y+1)\\ \\ \end{align*}\\ \\ \def\MA{x^2} \def\MBF{+} \def\MB{(3y-1)x} \def\MCF{+} \def\MC{(y-2)(2y+1)} \def\SLA{x} \def\SLF{+} \def\SLB{(y-2)} \def\SRA{x} \def\SRF{+} \def\SRB{(2y+1)} \def\SRALB{(y-2)x} \def\SLARB{(2y+1)x} \begin{align*} \colMM{red}{\fbox{②たすきがけ※} } & \end{align*} \\ \begin{alignedat}{3} \colBX{bisque}{$\SLA$} & & \colBX{palegreen}{$\SLB$} && \colBX{palegreen}{$\SRALB$}\\ \colBX{palegreen}{$\SRA$} & & \colBX{bisque}{$\SRB$} && \colBX{bisque}{$\SLARB$}\\\hline \MA & & \MC && \MB\\ \colMM{red}{\bf 先頭} & & \colMM{red}{\bf 最後} && \colMM{red}{\bf 真ん中} \end{alignedat}\\ %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
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【解答】次数引き分け➡xで整理
\def\S{3x^2-2xy-y^2-11x-y+6} \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*} & \S\\ & \colMM{red}{ \Darr x\ (の個数)で整理!}\\ &= 3x^2+(-2xy-11x)+(-y^2-y+6)\\ & \colMM{orange}{ ①共通\Darr }\colMM{green}{ \Darr ①マイナスを外へ}\\ &= 3x^2+(-2y-11)x-(y^2+y-6)\\ & \colMM{green}{ \Darr ②たすきがけ}\\ &= 3x^2+(-2y-11)x-(y-2)(y+3)\colMM{red}{\Leftarrow x\ の2次式!}\\ & \colMM{red}{ \Darr ②たすきがけ※}\\ &= \left\{x-(y+3)\right\}\left\{3x+(y-2)\right\}\\ \\ &= (x-y-3)(3x+y-2)\\ \\ \end{align*}\\ \\ \def\MA{3x^2} \def\MBF{} \def\MB{(-2y-11)x} \def\MCF{} \def\MC{-(y-2)(y+3)} \def\SLA{x} \def\SLF{} \def\SLB{-(y+3)} \def\SRA{3x} \def\SRF{+} \def\SRB{(y-2)} \def\SRALB{(-3y-9)x} \def\SLARB{(y-2)x} \begin{align*} \colMM{red}{\fbox{②たすきがけ※} } & \end{align*} \\ \begin{alignedat}{3} \colBX{bisque}{$\SLA$} & & \colBX{palegreen}{$\SLB$} && \colBX{palegreen}{$\SRALB$}\\ \colBX{palegreen}{$\SRA$} & & \colBX{bisque}{$\SRB$} && \colBX{bisque}{$\SLARB$}\\\hline \MA & & \MC && \MB\\ \colMM{red}{\bf 先頭} & & \colMM{red}{\bf 最後} && \colMM{red}{\bf 真ん中} \end{alignedat}\\ %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
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【解答】次数引き分け➡xで整理
\def\S{x^2-5xy+4y^2+x+2y-2} \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*} & \S\\ & \colMM{red}{ \Darr x\ (の個数)で整理!}\\ &= x^2+(-5xy+x)+(4y^2+2y-2)\\ & \colMM{orange}{ ①共通\Darr }\colMM{green}{ \Darr ①共通}\\ &= x^2+(-5y+1)x+2(2y^2+y-1)\\ & \colMM{green}{ \Darr ②たすきがけ}\\ &= x^2+(-5y+1)x+2(y+1)(2y-1)\colMM{red}{\Leftarrow x\ の2次式!}\\ & \colMM{red}{ \Darr ②たすきがけ※}\\ &= \left\{x-(y+1)\right\}\left\{x-2(2y-1)\right\}\\ \\ &= (x-y-1)(x-4y+2)\\ \\ \end{align*}\\ \\ \def\MA{x^2} \def\MBF{+} \def\MB{(-5y+1)x} \def\MCF{+} \def\MC{2(y+1)(2y-1)} \def\SLA{x} \def\SLF{} \def\SLB{-(y+1)} \def\SRA{x} \def\SRF{+} \def\SRB{-2(2y-1)} \def\SRALB{(-y-1)x} \def\SLARB{(-4y+2)x} \begin{align*} \colMM{red}{\fbox{②たすきがけ※} } & \end{align*} \\ \begin{alignedat}{3} \colBX{bisque}{$\SLA$} & & \colBX{palegreen}{$\SLB$} && \colBX{palegreen}{$\SRALB$}\\ \colBX{palegreen}{$\SRA$} & & \colBX{bisque}{$\SRB$} && \colBX{bisque}{$\SLARB$}\\\hline \MA & & \MC && \MB\\ \colMM{red}{\bf 先頭} & & \colMM{red}{\bf 最後} && \colMM{red}{\bf 真ん中} \end{alignedat}\\ %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan