erweitern ((x^3+1)^3)/(9x^2)

Lösung

erweitern

\frac{( x ^{3} + 1 ) ^{3}}{9 x ^{2}}

\frac{x ^{7}}{9} + \frac{x ^{4}}{3} + \frac{x}{3} + \frac{1}{9 x ^{2}}

Schritte zur Lösung

\frac{( x ^{3} + 1 ) ^{3}}{9 x ^{2}}

(x^{3} + 1)^{3} = x^{9} + 3 x^{6} + 3 x^{3} + 1

= \frac{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}{9 x ^{2}}

Wende Bruchregel an:

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

\frac{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}{9 x ^{2}} = \frac{x ^{9}}{9 x ^{2}} + \frac{3 x ^{6}}{9 x ^{2}} + \frac{3 x ^{3}}{9 x ^{2}} + \frac{1}{9 x ^{2}}

= \frac{x ^{9}}{9 x ^{2}} + \frac{3 x ^{6}}{9 x ^{2}} + \frac{3 x ^{3}}{9 x ^{2}} + \frac{1}{9 x ^{2}}

Streiche

\frac{x ^{9}}{9 x ^{2}} : \frac{x ^{7}}{9}

= \frac{x ^{7}}{9} + \frac{3 x ^{6}}{9 x ^{2}} + \frac{3 x ^{3}}{9 x ^{2}} + \frac{1}{9 x ^{2}}

Streiche

\frac{3 x ^{6}}{9 x ^{2}} : \frac{x ^{4}}{3}

= \frac{x ^{7}}{9} + \frac{x ^{4}}{3} + \frac{3 x ^{3}}{9 x ^{2}} + \frac{1}{9 x ^{2}}

Streiche

\frac{3 x ^{3}}{9 x ^{2}} : \frac{x}{3}

= \frac{x ^{7}}{9} + \frac{x ^{4}}{3} + \frac{x}{3} + \frac{1}{9 x ^{2}}

e x p an d g (f (x + 1))

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

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

e x p an d (1, - 4, 1) x (2, 3, 0)

e x p an d (- 17) \times (6)