展开 (100(0.02x+4)^3)/x

解答

展开

\frac{100 ( 0.02 x + 4 ) ^{3}}{x}

0.0008 x^{2} + 0.48 x + 96 + \frac{6400}{x}

求解步骤

\frac{100 ( 0.02 x + 4 ) ^{3}}{x}

(0.02 x + 4)^{3} = 0.000008 x^{3} + 0.0048 x^{2} + 0.96 x + 64

= \frac{100 ( 0.000008 x ^{3} + 0.0048 x ^{2} + 0.96 x + 64 )}{x}

乘开

100 (0.000008 x^{3} + 0.0048 x^{2} + 0.96 x + 64) : 0.0008 x^{3} + 0.48 x^{2} + 96 x + 6400

= \frac{0.0008 x ^{3} + 0.48 x ^{2} + 96 x + 6400}{x}

使用分式法则:

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

\frac{0.0008 x ^{3} + 0.48 x ^{2} + 96 x + 6400}{x} = \frac{0.0008 x ^{3}}{x} + \frac{0.48 x ^{2}}{x} + \frac{96 x}{x} + \frac{6400}{x}

= \frac{0.0008 x ^{3}}{x} + \frac{0.48 x ^{2}}{x} + \frac{96 x}{x} + \frac{6400}{x}

消掉

\frac{0.0008 x ^{3}}{x} : 0.0008 x^{2}

= 0.0008 x^{2} + \frac{0.48 x ^{2}}{x} + \frac{96 x}{x} + \frac{6400}{x}

消掉

\frac{0.48 x ^{2}}{x} : 0.48 x

= 0.0008 x^{2} + 0.48 x + \frac{96 x}{x} + \frac{6400}{x}

消掉

\frac{96 x}{x} : 96

= 0.0008 x^{2} + 0.48 x + 96 + \frac{6400}{x}

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