展開する (x^2+2)(2x-1/x)^4

解

展開する

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

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

解答ステップ

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

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

分配法則を適用する:

a (b + c) = ab + a c

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

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

簡素化

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

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