展開する (2x^2+1)*(x-2/x)^4

解

展開する

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

\frac{2 ( x ^{2} - 2 ) ^{4}}{x ^{2}} + \frac{( x ^{2} - 2 ) ^{4}}{x ^{4}}

解答ステップ

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

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

分配法則を適用する:

a (b + c) = ab + a c

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

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

簡素化

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

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