展開する x^{4/5}(x-2)^2

解

展開する

x^{\frac{4}{5}} (x - 2)^{2}

x^{\frac{14}{5}} - 4 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 4

解答ステップ

x^{\frac{4}{5}} (x - 2)^{2}

拡張

(x - 2)^{2} : x^{2} - 4 x + 4

= x^{\frac{4}{5}} (x^{2} - 4 x + 4)

分配法則を適用する:

m (a + b + c) = ma + mb + m c

x^{\frac{4}{5}} (x^{2} - 4 x + 4) = x^{\frac{4}{5}} x^{2} + x^{\frac{4}{5}} (- 4 x) + x^{\frac{4}{5}} \cdot 4

= x^{\frac{4}{5}} x^{2} + x^{\frac{4}{5}} (- 4 x) + x^{\frac{4}{5}} \cdot 4

x^{\frac{4}{5}} x^{2} = x^{\frac{14}{5}}

x^{\frac{4}{5}} (- 4 x) = - 4 x^{\frac{9}{5}}

= x^{\frac{14}{5}} - 4 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 4