展開する (40(2-x^{1/5})^3)/3

解

展開する

\frac{40 ( 2 - x ^{\frac{1}{5}} ) ^{3}}{3}

\frac{320}{3} - 160 x^{\frac{1}{5}} + 80 x^{\frac{2}{5}} - \frac{40 x ^{\frac{3}{5}}}{3}

解答ステップ

\frac{40 ( 2 - x ^{\frac{1}{5}} ) ^{3}}{3}

(2 - x^{\frac{1}{5}})^{3} = 8 - 12 x^{\frac{1}{5}} + 6 x^{\frac{2}{5}} - x^{\frac{3}{5}}

= \frac{40 ( 6 x ^{\frac{2}{5}} - 12 x ^{\frac{1}{5}} - x ^{\frac{3}{5}} + 8 )}{3}

拡張

40 (8 - 12 x^{\frac{1}{5}} + 6 x^{\frac{2}{5}} - x^{\frac{3}{5}}) : 320 - 480 x^{\frac{1}{5}} + 240 x^{\frac{2}{5}} - 40 x^{\frac{3}{5}}

= \frac{320 - 480 x ^{\frac{1}{5}} + 240 x ^{\frac{2}{5}} - 40 x ^{\frac{3}{5}}}{3}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{320 - 480 x ^{\frac{1}{5}} + 240 x ^{\frac{2}{5}} - 40 x ^{\frac{3}{5}}}{3} = \frac{320}{3} - \frac{480 x ^{\frac{1}{5}}}{3} + \frac{240 x ^{\frac{2}{5}}}{3} - \frac{40 x ^{\frac{3}{5}}}{3}

= \frac{320}{3} - \frac{480 x ^{\frac{1}{5}}}{3} + \frac{240 x ^{\frac{2}{5}}}{3} - \frac{40 x ^{\frac{3}{5}}}{3}

数を割る:

\frac{480}{3} = 160

= \frac{320}{3} - 160 x^{\frac{1}{5}} + \frac{240 x ^{\frac{2}{5}}}{3} - \frac{40 x ^{\frac{3}{5}}}{3}

数を割る:

\frac{240}{3} = 80

= \frac{320}{3} - 160 x^{\frac{1}{5}} + 80 x^{\frac{2}{5}} - \frac{40 x ^{\frac{3}{5}}}{3}