展开 ((x^4-4)^2)/(16x^4)

解答

展开

\frac{( x ^{4} - 4 ) ^{2}}{16 x ^{4}}

\frac{x ^{4}}{16} - \frac{1}{2} + \frac{1}{x ^{4}}

求解步骤

\frac{( x ^{4} - 4 ) ^{2}}{16 x ^{4}}

(x^{4} - 4)^{2} = x^{8} - 8 x^{4} + 16

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

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

消掉

\frac{x ^{8}}{16 x ^{4}} : \frac{x ^{4}}{16}

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

消掉

\frac{8 x ^{4}}{16 x ^{4}} : \frac{1}{2}

= \frac{x ^{4}}{16} - \frac{1}{2} + \frac{16}{16 x ^{4}}

数字相除:

\frac{16}{16} = 1

= \frac{x ^{4}}{16} - \frac{1}{2} + \frac{1}{x ^{4}}

e x p an d Dr (π r^{2} + a r)

e x p an d \frac{1}{( 1 + 5 x ) ^{4}}

e x p an d - 3 i x^{2} + (2 + 2 i) x + 2

e x p an d \frac{x}{e ^{x^{2} - \frac{1}{2} x^{4} + \frac{1}{3} x^{6}}}

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