展開する 1/(x^3)(1/(x^2)-2x)^9

解

展開する

\frac{1}{x ^{3}} (\frac{1}{x ^{2}} - 2 x)^{9}

\frac{1}{x ^{21}} - \frac{18}{x ^{18}} + \frac{144}{x ^{15}} - \frac{672}{x ^{12}} + \frac{2016}{x ^{9}} - \frac{4032}{x ^{6}} + \frac{5376}{x ^{3}} - 4608 + 2304 x^{3} - 512 x^{6}

解答ステップ

\frac{1}{x ^{3}} (\frac{1}{x ^{2}} - 2 x)^{9}

拡張

(\frac{1}{x ^{2}} - 2 x)^{9} : \frac{1}{x ^{18}} - \frac{18}{x ^{15}} + \frac{144}{x ^{12}} - \frac{672}{x ^{9}} + \frac{2016}{x ^{6}} - \frac{4032}{x ^{3}} + 5376 - 4608 x^{3} + 2304 x^{6} - 512 x^{9}

= \frac{1}{x ^{3}} (\frac{1}{x ^{18}} - \frac{18}{x ^{15}} + \frac{144}{x ^{12}} - \frac{672}{x ^{9}} + \frac{2016}{x ^{6}} - \frac{4032}{x ^{3}} + 5376 - 4608 x^{3} + 2304 x^{6} - 512 x^{9})

括弧を分配する

= \frac{1}{x ^{3}} \cdot \frac{1}{x ^{18}} + \frac{1}{x ^{3}} (- \frac{18}{x ^{15}}) + \frac{1}{x ^{3}} \cdot \frac{144}{x ^{12}} + \frac{1}{x ^{3}} (- \frac{672}{x ^{9}}) + \frac{1}{x ^{3}} \cdot \frac{2016}{x ^{6}} + \frac{1}{x ^{3}} (- \frac{4032}{x ^{3}}) + \frac{1}{x ^{3}} \cdot 5376 + \frac{1}{x ^{3}} (- 4608 x^{3}) + \frac{1}{x ^{3}} \cdot 2304 x^{6} + \frac{1}{x ^{3}} (- 512 x^{9})

簡素化

\frac{1}{x ^{3}} \cdot \frac{1}{x ^{18}} + \frac{1}{x ^{3}} (- \frac{18}{x ^{15}}) + \frac{1}{x ^{3}} \cdot \frac{144}{x ^{12}} + \frac{1}{x ^{3}} (- \frac{672}{x ^{9}}) + \frac{1}{x ^{3}} \cdot \frac{2016}{x ^{6}} + \frac{1}{x ^{3}} (- \frac{4032}{x ^{3}}) + \frac{1}{x ^{3}} \cdot 5376 + \frac{1}{x ^{3}} (- 4608 x^{3}) + \frac{1}{x ^{3}} \cdot 2304 x^{6} + \frac{1}{x ^{3}} (- 512 x^{9}) : \frac{1}{x ^{21}} - \frac{18}{x ^{18}} + \frac{144}{x ^{15}} - \frac{672}{x ^{12}} + \frac{2016}{x ^{9}} - \frac{4032}{x ^{6}} + \frac{5376}{x ^{3}} - 4608 + 2304 x^{3} - 512 x^{6}

= \frac{1}{x ^{21}} - \frac{18}{x ^{18}} + \frac{144}{x ^{15}} - \frac{672}{x ^{12}} + \frac{2016}{x ^{9}} - \frac{4032}{x ^{6}} + \frac{5376}{x ^{3}} - 4608 + 2304 x^{3} - 512 x^{6}