展開する (2(-8x^3+72x^2-216x+216))/(27)

解

展開する

\frac{2 ( - 8 x ^{3} + 72 x ^{2} - 216 x + 216 )}{27}

- \frac{16 x ^{3}}{27} + \frac{16 x ^{2}}{3} - 16 x + 16

解答ステップ

\frac{2 ( - 8 x ^{3} + 72 x ^{2} - 216 x + 216 )}{27}

拡張

2 (- 8 x^{3} + 72 x^{2} - 216 x + 216) : - 16 x^{3} + 144 x^{2} - 432 x + 432

= \frac{- 16 x ^{3} + 144 x ^{2} - 432 x + 432}{27}

分数の規則を適用する:

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

\frac{- 16 x ^{3} + 144 x ^{2} - 432 x + 432}{27} = - \frac{16 x ^{3}}{27} + \frac{144 x ^{2}}{27} - \frac{432 x}{27} + \frac{432}{27}

= - \frac{16 x ^{3}}{27} + \frac{144 x ^{2}}{27} - \frac{432 x}{27} + \frac{432}{27}

キャンセル

\frac{144 x ^{2}}{27} : \frac{16 x ^{2}}{3}

= - \frac{16 x ^{3}}{27} + \frac{16 x ^{2}}{3} - \frac{432 x}{27} + \frac{432}{27}

数を割る:

\frac{432}{27} = 16

= - \frac{16 x ^{3}}{27} + \frac{16 x ^{2}}{3} - 16 x + 16