展開する x^{4/5}(8x-32)^2

解

展開する

x^{\frac{4}{5}} (8 x - 32)^{2}

64 x^{\frac{14}{5}} - 512 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 1024

解答ステップ

x^{\frac{4}{5}} (8 x - 32)^{2}

拡張

(8 x - 32)^{2} : 64 x^{2} - 512 x + 1024

= x^{\frac{4}{5}} (64 x^{2} - 512 x + 1024)

分配法則を適用する:

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

x^{\frac{4}{5}} (64 x^{2} - 512 x + 1024) = x^{\frac{4}{5}} \cdot 64 x^{2} + x^{\frac{4}{5}} (- 512 x) + x^{\frac{4}{5}} \cdot 1024

= x^{\frac{4}{5}} \cdot 64 x^{2} + x^{\frac{4}{5}} (- 512 x) + x^{\frac{4}{5}} \cdot 1024

x^{\frac{4}{5}} \cdot 64 x^{2} = 64 x^{\frac{14}{5}}

x^{\frac{4}{5}} (- 512 x) = - 512 x^{\frac{9}{5}}

= 64 x^{\frac{14}{5}} - 512 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 1024