展开 ((x+2)(4x-1)^2)/(x^3)

解答

展开

\frac{( x + 2 ) ( 4 x - 1 ) ^{2}}{x ^{3}}

16 + \frac{24}{x} - \frac{15}{x ^{2}} + \frac{2}{x ^{3}}

求解步骤

\frac{( x + 2 ) ( 4 x - 1 ) ^{2}}{x ^{3}}

(4 x - 1)^{2} = 16 x^{2} - 8 x + 1

= \frac{( x + 2 ) ( 16 x ^{2} - 8 x + 1 )}{x ^{3}}

乘开

(x + 2) (16 x^{2} - 8 x + 1) : 16 x^{3} + 24 x^{2} - 15 x + 2

= \frac{16 x ^{3} + 24 x ^{2} - 15 x + 2}{x ^{3}}

使用分式法则:

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

\frac{16 x ^{3} + 24 x ^{2} - 15 x + 2}{x ^{3}} = \frac{16 x ^{3}}{x ^{3}} + \frac{24 x ^{2}}{x ^{3}} - \frac{15 x}{x ^{3}} + \frac{2}{x ^{3}}

= \frac{16 x ^{3}}{x ^{3}} + \frac{24 x ^{2}}{x ^{3}} - \frac{15 x}{x ^{3}} + \frac{2}{x ^{3}}

消掉

\frac{16 x ^{3}}{x ^{3}} : 16

= 16 + \frac{24 x ^{2}}{x ^{3}} - \frac{15 x}{x ^{3}} + \frac{2}{x ^{3}}

消掉

\frac{24 x ^{2}}{x ^{3}} : \frac{24}{x}

= 16 + \frac{24}{x} - \frac{15 x}{x ^{3}} + \frac{2}{x ^{3}}

消掉

\frac{15 x}{x ^{3}} : \frac{15}{x ^{2}}

= 16 + \frac{24}{x} - \frac{15}{x ^{2}} + \frac{2}{x ^{3}}

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