展开 ((n+2x)/n)^3

解答

展开

(\frac{n + 2 x}{n})^{3}

1 + \frac{6 x}{n} + \frac{12 x ^{2}}{n ^{2}} + \frac{8 x ^{3}}{n ^{3}}

求解步骤

(\frac{n + 2 x}{n})^{3}

使用指数法则:

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

= \frac{( n + 2 x ) ^{3}}{n ^{3}}

(n + 2 x)^{3} = n^{3} + 6 n^{2} x + 12 n x^{2} + 8 x^{3}

= \frac{n ^{3} + 6 n ^{2} x + 12 n x ^{2} + 8 x ^{3}}{n ^{3}}

使用分式法则:

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

\frac{n ^{3} + 6 n ^{2} x + 12 n x ^{2} + 8 x ^{3}}{n ^{3}} = \frac{n ^{3}}{n ^{3}} + \frac{6 n ^{2} x}{n ^{3}} + \frac{12 n x ^{2}}{n ^{3}} + \frac{8 x ^{3}}{n ^{3}}

= \frac{n ^{3}}{n ^{3}} + \frac{6 n ^{2} x}{n ^{3}} + \frac{12 n x ^{2}}{n ^{3}} + \frac{8 x ^{3}}{n ^{3}}

使用法则

\frac{a}{a} = 1

\frac{n ^{3}}{n ^{3}} = 1

= 1 + \frac{6 n ^{2} x}{n ^{3}} + \frac{12 n x ^{2}}{n ^{3}} + \frac{8 x ^{3}}{n ^{3}}

消掉

\frac{6 n ^{2} x}{n ^{3}} : \frac{6 x}{n}

= 1 + \frac{6 x}{n} + \frac{12 n x ^{2}}{n ^{3}} + \frac{8 x ^{3}}{n ^{3}}

消掉

\frac{12 n x ^{2}}{n ^{3}} : \frac{12 x ^{2}}{n ^{2}}

= 1 + \frac{6 x}{n} + \frac{12 x ^{2}}{n ^{2}} + \frac{8 x ^{3}}{n ^{3}}

e x p an d - \frac{8 - 2 x ^{2} ( 4 - x ^{2} )}{3}

e x p an d (\frac{1}{3} x + \frac{2}{3} y)^{2}

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

e x p an d 3 l e f t (c - 6 b + 6 z)

s im pl i f y (2 x + 2 x^{2} - y)^{2}