展開する x^{4/5}× (x-4)^2

解

展開する

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

x^{\frac{14}{5}} - 8 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 16

解答ステップ

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

拡張

(x - 4)^{2} : x^{2} - 8 x + 16

= x^{\frac{4}{5}} (x^{2} - 8 x + 16)

分配法則を適用する:

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

x^{\frac{4}{5}} (x^{2} - 8 x + 16) = x^{\frac{4}{5}} x^{2} + x^{\frac{4}{5}} (- 8 x) + x^{\frac{4}{5}} \cdot 16

= x^{\frac{4}{5}} x^{2} + x^{\frac{4}{5}} (- 8 x) + x^{\frac{4}{5}} \cdot 16

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

x^{\frac{4}{5}} (- 8 x) = - 8 x^{\frac{9}{5}}

= x^{\frac{14}{5}} - 8 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 16