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\SL{2x} \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*} & \colBX{bisque}{$\SL$}(x^2+2x-3)\\ \\ &= \colBX{bisque}{$\SL$} \cdot x^2 + \colBX{bisque}{$\SL$} \cdot 2x + \colBX{bisque}{$\SL$} \cdot (-3)\\ \\ &= 2x^3+4x^2-6x \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\SL{x^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*} & \colBX{bisque}{$\SL$}(x^2-3x+4)\\ \\ &= \colBX{bisque}{$\SL$} \cdot x^2 + \colBX{bisque}{$\SL$} \cdot (-3x) + \colBX{bisque}{$\SL$} \cdot 4\\ \\ &= x^4-3x^3+4x^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】
\def\SL{2x^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*} & \colBX{bisque}{$\SL$}(x^2+2x-1)\\ \\ &= \colBX{bisque}{$\SL$} \cdot x^2 + \colBX{bisque}{$\SL$} \cdot 2x + \colBX{bisque}{$\SL$} \cdot (-1)\\ \\ &= 2x^4+4x^3-2x^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】
\def\SR{xy^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*} & (x^3-6y)\colBX{bisque}{$\SR$}\\ \\ &= x^3 \cdot \colBX{bisque}{$\SR$} -6y \cdot \colBX{bisque}{$\SR$}\\ \\ &= x^4y^2-6xy^3 \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\SR{x^2y} \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*} & (xy+3)\colBX{bisque}{$\SR$}\\ \\ &= xy \cdot \colBX{bisque}{$\SR$} +3 \cdot \colBX{bisque}{$\SR$}\\ \\ &= x^3y^2+3x^2y \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\SR{ab^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*} & (a^2-ab)\colBX{bisque}{$\SR$}\\ \\ &= a^2 \cdot \colBX{bisque}{$\SR$} -ab \cdot \colBX{bisque}{$\SR$}\\ \\ &= a^3b^2-a^2b^3 \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】前から
\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*} & (\colBX{bisque}{$2x$}\,\colBX{palegreen}{$-3$})(3x^2-x+1)\\ \\ &= \colBX{bisque}{$2x$}(3x^2-x+1)\colBX{palegreen}{$-3$}(3x^2-x+1)\\ \\ &= (6x^3-2x^2+2x)+(-9x^2+3x-3)\\ \\ &= 6x^3-2x^2+2x-9x^2+3x-3\\ \\ &\color{lightgray}= 6x^3+(-2x^2-9x^2)+(2x+3x)-3\\ \\ &= 6x^3-11x^2+5x-3 \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
【解答】後ろから
\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*} & (2x-3)(\colBX{bisque}{$3x^2$}\,\colBX{palegreen}{$-x$}\,\colBX{violet}{$+1$})\\ \\ &= (2x-3) \colBX{bisque}{$3x^2$}+(2x-3)\colBX{palegreen}{$(-x)$}+(2x-3)\colBX{violet}{$(+1)$}\\ \\ &= (6x^3-9x^2)+(-2x^2+3x)+(2x-3)\\ \\ &= 6x^3-9x^2-2x^2+3x+2x-3\\ \\ &\color{lightgray}= 6x^3+(-9x^2-2x^2)+(3x+2x)-3\\ \\ &= 6x^3-11x^2+5x-3 \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】前から
\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*} & (\colBX{bisque}{$3x$}\,\colBX{palegreen}{$-1$})(2x^2-x+5)\\ \\ &= \colBX{bisque}{$3x$}(2x^2-x+5)\colBX{palegreen}{$-1$}(2x^2-x+5)\\ \\ &= (6x^3-3x^2+15x)+(-2x^2+x-5)\\ \\ &= 6x^3-3x^2+15x-2x^2+x-5\\ \\ &\color{lightgray}= 6x^3+(-3x^2-2x^2)+(15x+x)-5\\ \\ &= 6x^3-5x^2+16x-5 \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
【解答】後ろから
\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*} & (3x-1)(\colBX{bisque}{$2x^2$}\,\colBX{palegreen}{$-x$}\,\colBX{violet}{$+5$})\\ \\ &= (3x-1) \colBX{bisque}{$2x^2$}+(3x-1)\colBX{palegreen}{$(-x)$}+(3x-1)\colBX{violet}{$(+5)$}\\ \\ &= (6x^3-2x^2)+(-3x^2+x)+(15x-5)\\ \\ &= 6x^3-2x^2-3x^2+x+15x-5\\ \\ &\color{lightgray}= 6x^3+(-2x^2-3x^2)+(x+15x)-5\\ \\ &= 6x^3-5x^2+16x-5 \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】前から
\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*} & (\colBX{bisque}{$3x$}\,\colBX{palegreen}{$-1$})(x^2-2x+3)\\ \\ &= \colBX{bisque}{$3x$}(x^2-2x+3)\colBX{palegreen}{$-1$}(x^2-2x+3)\\ \\ &= (3x^3-6x^2+9x)+(-x^2+2x-3)\\ \\ &= 3x^3-6x^2+9x-x^2+2x-3\\ \\ &\color{lightgray}= 3x^3+(-6x^2-x^2)+(9x+2x)-3\\ \\ &= 3x^3-7x^2+11x-3 \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
【解答】後ろから
\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*} & (3x-1)(\colBX{bisque}{$x^2$}\,\colBX{palegreen}{$-2x$}\,\colBX{violet}{$+3$})\\ \\ &= (3x-1) \colBX{bisque}{$x^2$}+(3x-1)\colBX{palegreen}{$(-2x)$}+(3x-1)\colBX{violet}{$(+3)$}\\ \\ &= (3x^3-x^2)+(-6x^2+2x)+(9x-3)\\ \\ &= 3x^3-x^2-6x^2+2x+9x-3\\ \\ &\color{lightgray}= 3x^3+(-x^2-6x^2)+(2x+9x)-3\\ \\ &= 3x^3-7x^2+11x-3 \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan