erweitern (2(216-216x+72x^2-8x^3))/(27)

Lösung

erweitern

\frac{2 ( 216 - 216 x + 72 x ^{2} - 8 x ^{3} )}{27}

- \frac{16 x ^{3}}{27} + \frac{16 x ^{2}}{3} - 16 x + 16

Schritte zur Lösung

\frac{2 ( 216 - 216 x + 72 x ^{2} - 8 x ^{3} )}{27}

Multipliziere aus

2 (216 - 216 x + 72 x^{2} - 8 x^{3}) : 432 - 432 x + 144 x^{2} - 16 x^{3}

= \frac{432 - 432 x + 144 x ^{2} - 16 x ^{3}}{27}

Wende Bruchregel an:

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

\frac{432 - 432 x + 144 x ^{2} - 16 x ^{3}}{27} = \frac{432}{27} - \frac{432 x}{27} + \frac{144 x ^{2}}{27} - \frac{16 x ^{3}}{27}

= \frac{432}{27} - \frac{432 x}{27} + \frac{144 x ^{2}}{27} - \frac{16 x ^{3}}{27}

Teile die Zahlen:

\frac{432}{27} = 16

= 16 - 16 x + \frac{144 x ^{2}}{27} - \frac{16 x ^{3}}{27}

Streiche

\frac{144 x ^{2}}{27} : \frac{16 x ^{2}}{3}

= 16 - 16 x + \frac{16 x ^{2}}{3} - \frac{16 x ^{3}}{27}

Rewrite in standard form

= - \frac{16 x ^{3}}{27} + \frac{16 x ^{2}}{3} - 16 x + 16

e x p an d \frac{x ^{3} + 16}{( x + 2 ) ^{2}}

e x p an d \frac{A ( x - 2 ) + B}{( x - 2 ) ^{2}}

e x p an d 28

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

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