展開する (8x^{3/4}-2x^5)^2

解

展開する

(8 x^{\frac{3}{4}} - 2 x^{5})^{2}

64 x^{\frac{3}{2}} - 32 x^{\frac{23}{4}} + 4 x^{10}

解答ステップ

(8 x^{\frac{3}{4}} - 2 x^{5})^{2}

完全平方式を適用する:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(8 x^{\frac{3}{4}} - 2 x^{5})^{2} = (8 x^{\frac{3}{4}})^{2} - 2 \cdot 8 x^{\frac{3}{4}} \cdot 2 x^{5} + (2 x^{5})^{2}

= (8 x^{\frac{3}{4}})^{2} - 2 \cdot 8 x^{\frac{3}{4}} \cdot 2 x^{5} + (2 x^{5})^{2}

(8 x^{\frac{3}{4}})^{2} = 64 x^{\frac{3}{2}}

2 \cdot 8 x^{\frac{3}{4}} \cdot 2 x^{5} = 32 x^{\frac{23}{4}}

(2 x^{5})^{2} = 4 x^{10}

= 64 x^{\frac{3}{2}} - 32 x^{\frac{23}{4}} + 4 x^{10}