展開する (arctan(sqrt(x-2))-5x^{3/2})^2

解

展開する

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

arctan^{2} (x - 2) - 10 x^{\frac{3}{2}} arctan (x - 2) + 25 x^{3}

解答ステップ

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

完全平方式を適用する:

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

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

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

2 arctan (x - 2) \cdot 5 x^{\frac{3}{2}} = 10 x^{\frac{3}{2}} arctan (x - 2)

(5 x^{\frac{3}{2}})^{2} = 25 x^{3}

= arctan^{2} (x - 2) - 10 x^{\frac{3}{2}} arctan (x - 2) + 25 x^{3}