展開する (1/4 x^2-1/(x^2))^2

解

展開する

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

\frac{x ^{8} - 8 x ^{4} + 16}{16 x ^{4}}

解答ステップ

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

完全平方式を適用する:

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

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

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

簡素化

(\frac{1}{4} x^{2})^{2} - 2 \cdot \frac{1}{4} x^{2} \frac{1}{x ^{2}} + (\frac{1}{x ^{2}})^{2} : \frac{x ^{8} - 8 x ^{4} + 16}{16 x ^{4}}

= \frac{x ^{8} - 8 x ^{4} + 16}{16 x ^{4}}