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受欢迎的代数 >

展开 ((x+2)/x)^4

解答

展开

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

解答

1 + \frac{8}{x} + \frac{24}{x ^{2}} + \frac{32}{x ^{3}} + \frac{16}{x ^{4}}

求解步骤

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

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

(x + 2)^{4} = x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16

= \frac{x ^{4} + 8 x ^{3} + 24 x ^{2} + 32 x + 16}{x ^{4}}

使用分式法则:

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

\frac{x ^{4} + 8 x ^{3} + 24 x ^{2} + 32 x + 16}{x ^{4}} = \frac{x ^{4}}{x ^{4}} + \frac{8 x ^{3}}{x ^{4}} + \frac{24 x ^{2}}{x ^{4}} + \frac{32 x}{x ^{4}} + \frac{16}{x ^{4}}

= \frac{x ^{4}}{x ^{4}} + \frac{8 x ^{3}}{x ^{4}} + \frac{24 x ^{2}}{x ^{4}} + \frac{32 x}{x ^{4}} + \frac{16}{x ^{4}}

使用法则

\frac{a}{a} = 1

\frac{x ^{4}}{x ^{4}} = 1

= 1 + \frac{8 x ^{3}}{x ^{4}} + \frac{24 x ^{2}}{x ^{4}} + \frac{32 x}{x ^{4}} + \frac{16}{x ^{4}}

消掉

\frac{8 x ^{3}}{x ^{4}} : \frac{8}{x}

= 1 + \frac{8}{x} + \frac{24 x ^{2}}{x ^{4}} + \frac{32 x}{x ^{4}} + \frac{16}{x ^{4}}

消掉

\frac{24 x ^{2}}{x ^{4}} : \frac{24}{x ^{2}}

= 1 + \frac{8}{x} + \frac{24}{x ^{2}} + \frac{32 x}{x ^{4}} + \frac{16}{x ^{4}}

消掉

\frac{32 x}{x ^{4}} : \frac{32}{x ^{3}}

= 1 + \frac{8}{x} + \frac{24}{x ^{2}} + \frac{32}{x ^{3}} + \frac{16}{x ^{4}}

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