展开 ((x^3+1)^2)/(x^3)

解答

展开

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

x^{3} + 2 + \frac{1}{x ^{3}}

求解步骤

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

(x^{3} + 1)^{2} = x^{6} + 2 x^{3} + 1

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

使用分式法则:

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

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

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

消掉

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

= x^{3} + \frac{2 x ^{3}}{x ^{3}} + \frac{1}{x ^{3}}

消掉

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

= x^{3} + 2 + \frac{1}{x ^{3}}

e x p an d a c - b d + i (a d + b c)

e x p an d \frac{( x y ^{2} )}{z ^{4}}

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

e x p an d 8 (6 x^{3} + 4 x^{2} - x)^{3}

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