展開する x^{4/5}(10x-40)^2

解

展開する

x^{\frac{4}{5}} (10 x - 40)^{2}

100 x^{\frac{14}{5}} - 800 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 1600

解答ステップ

x^{\frac{4}{5}} (10 x - 40)^{2}

拡張

(10 x - 40)^{2} : 100 x^{2} - 800 x + 1600

= x^{\frac{4}{5}} (100 x^{2} - 800 x + 1600)

分配法則を適用する:

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

x^{\frac{4}{5}} (100 x^{2} - 800 x + 1600) = x^{\frac{4}{5}} \cdot 100 x^{2} + x^{\frac{4}{5}} (- 800 x) + x^{\frac{4}{5}} \cdot 1600

= x^{\frac{4}{5}} \cdot 100 x^{2} + x^{\frac{4}{5}} (- 800 x) + x^{\frac{4}{5}} \cdot 1600

x^{\frac{4}{5}} \cdot 100 x^{2} = 100 x^{\frac{14}{5}}

x^{\frac{4}{5}} (- 800 x) = - 800 x^{\frac{9}{5}}

= 100 x^{\frac{14}{5}} - 800 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 1600