展开 ((x+6)^3)/(x^2)

解答

展开

\frac{( x + 6 ) ^{3}}{x ^{2}}

x + 18 + \frac{108}{x} + \frac{216}{x ^{2}}

求解步骤

\frac{( x + 6 ) ^{3}}{x ^{2}}

(x + 6)^{3} = x^{3} + 18 x^{2} + 108 x + 216

= \frac{x ^{3} + 18 x ^{2} + 108 x + 216}{x ^{2}}

使用分式法则:

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

\frac{x ^{3} + 18 x ^{2} + 108 x + 216}{x ^{2}} = \frac{x ^{3}}{x ^{2}} + \frac{18 x ^{2}}{x ^{2}} + \frac{108 x}{x ^{2}} + \frac{216}{x ^{2}}

= \frac{x ^{3}}{x ^{2}} + \frac{18 x ^{2}}{x ^{2}} + \frac{108 x}{x ^{2}} + \frac{216}{x ^{2}}

消掉

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

= x + \frac{18 x ^{2}}{x ^{2}} + \frac{108 x}{x ^{2}} + \frac{216}{x ^{2}}

消掉

\frac{18 x ^{2}}{x ^{2}} : 18

= x + 18 + \frac{108 x}{x ^{2}} + \frac{216}{x ^{2}}

消掉

\frac{108 x}{x ^{2}} : \frac{108}{x}

= x + 18 + \frac{108}{x} + \frac{216}{x ^{2}}

e x p an d 2 x (2 - ln (x))

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

\frac{d}{d t} ((P (t, M)) (r (t, M) P (t, M) (M - P (t, M))))

e x p an d (2 x - 1) \cdot lo g_{10} (5)

e x p an d x (x + 1) - (4 - x) (x + 1 = 6 (4 - x))