展開する (4x^{3/2}-2x^{1/2})^2

解

展開する

(4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})^{2}

16 x^{3} - 16 x^{2} + 4 x

解答ステップ

(4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})^{2}

完全平方式を適用する:

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

(4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})^{2} = (4 x^{\frac{3}{2}})^{2} - 2 \cdot 4 x^{\frac{3}{2}} \cdot 2 x^{\frac{1}{2}} + (2 x^{\frac{1}{2}})^{2}

= (4 x^{\frac{3}{2}})^{2} - 2 \cdot 4 x^{\frac{3}{2}} \cdot 2 x^{\frac{1}{2}} + (2 x^{\frac{1}{2}})^{2}

(4 x^{\frac{3}{2}})^{2} = 16 x^{3}

2 \cdot 4 x^{\frac{3}{2}} \cdot 2 x^{\frac{1}{2}} = 16 x^{2}

(2 x^{\frac{1}{2}})^{2} = 4 x

= 16 x^{3} - 16 x^{2} + 4 x