erweitern ((1+2e^t)^3)/(27)

Lösung

erweitern

\frac{( 1 + 2 e ^{t} ) ^{3}}{27}

\frac{1}{27} + \frac{2 e ^{t}}{9} + \frac{4 e ^{2 t}}{9} + \frac{8 e ^{3 t}}{27}

Schritte zur Lösung

\frac{( 1 + 2 e ^{t} ) ^{3}}{27}

(1 + 2 e^{t})^{3} = 1 + 6 e^{t} + 12 e^{2 t} + 8 e^{3 t}

= \frac{1 + 6 e ^{t} + 12 e ^{2 t} + 8 e ^{3 t}}{27}

Wende Bruchregel an:

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

\frac{1 + 6 e ^{t} + 12 e ^{2 t} + 8 e ^{3 t}}{27} = \frac{1}{27} + \frac{6 e ^{t}}{27} + \frac{12 e ^{2 t}}{27} + \frac{8 e ^{3 t}}{27}

= \frac{1}{27} + \frac{6 e ^{t}}{27} + \frac{12 e ^{2 t}}{27} + \frac{8 e ^{3 t}}{27}

Streiche

\frac{6 e ^{t}}{27} : \frac{2 e ^{t}}{9}

= \frac{1}{27} + \frac{2 e ^{t}}{9} + \frac{12 e ^{2 t}}{27} + \frac{8 e ^{3 t}}{27}

Streiche

\frac{12 e ^{2 t}}{27} : \frac{4 e ^{2 t}}{9}

= \frac{1}{27} + \frac{2 e ^{t}}{9} + \frac{4 e ^{2 t}}{9} + \frac{8 e ^{3 t}}{27}

e x p an d \frac{I n ( 2 - 3 x )}{x ^{2} - 36}

e x p an d (3 (n + 1))!

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

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

s im pl i f y (x + 1) (x - x + 1)