erweitern ((v-1)^3)/(v^2)

Lösung

erweitern

\frac{( v - 1 ) ^{3}}{v ^{2}}

v - 3 + \frac{3}{v} - \frac{1}{v ^{2}}

Schritte zur Lösung

\frac{( v - 1 ) ^{3}}{v ^{2}}

(v - 1)^{3} = v^{3} - 3 v^{2} + 3 v - 1

= \frac{v ^{3} - 3 v ^{2} + 3 v - 1}{v ^{2}}

Wende Bruchregel an:

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

\frac{v ^{3} - 3 v ^{2} + 3 v - 1}{v ^{2}} = \frac{v ^{3}}{v ^{2}} - \frac{3 v ^{2}}{v ^{2}} + \frac{3 v}{v ^{2}} - \frac{1}{v ^{2}}

= \frac{v ^{3}}{v ^{2}} - \frac{3 v ^{2}}{v ^{2}} + \frac{3 v}{v ^{2}} - \frac{1}{v ^{2}}

Streiche

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

= v - \frac{3 v ^{2}}{v ^{2}} + \frac{3 v}{v ^{2}} - \frac{1}{v ^{2}}

Streiche

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

= v - 3 + \frac{3 v}{v ^{2}} - \frac{1}{v ^{2}}

Streiche

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

= v - 3 + \frac{3}{v} - \frac{1}{v ^{2}}

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

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e x p an d l m (w x) - (3 x + 1) ln (x)