展開する x^{4/5}(7x-28)^2

解

展開する

x^{\frac{4}{5}} (7 x - 28)^{2}

49 x^{\frac{14}{5}} - 392 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 784

解答ステップ

x^{\frac{4}{5}} (7 x - 28)^{2}

拡張

(7 x - 28)^{2} : 49 x^{2} - 392 x + 784

= x^{\frac{4}{5}} (49 x^{2} - 392 x + 784)

分配法則を適用する:

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

x^{\frac{4}{5}} (49 x^{2} - 392 x + 784) = x^{\frac{4}{5}} \cdot 49 x^{2} + x^{\frac{4}{5}} (- 392 x) + x^{\frac{4}{5}} \cdot 784

= x^{\frac{4}{5}} \cdot 49 x^{2} + x^{\frac{4}{5}} (- 392 x) + x^{\frac{4}{5}} \cdot 784

x^{\frac{4}{5}} \cdot 49 x^{2} = 49 x^{\frac{14}{5}}

x^{\frac{4}{5}} (- 392 x) = - 392 x^{\frac{9}{5}}

= 49 x^{\frac{14}{5}} - 392 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 784