erweitern ((1+2sqrt(x))^4)/8

Lösung

erweitern

\frac{( 1 + 2 x ) ^{4}}{8}

\frac{1}{8} + x + 3 x + 4 x^{\frac{3}{2}} + 2 x^{2}

Schritte zur Lösung

\frac{( 1 + 2 x ) ^{4}}{8}

(1 + 2 x)^{4} = 1 + 8 x + 24 x + 32 x^{\frac{3}{2}} + 16 x^{2}

= \frac{1 + 8 x + 24 x + 32 x ^{\frac{3}{2}} + 16 x ^{2}}{8}

Wende Bruchregel an:

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

\frac{1 + 8 x + 24 x + 32 x ^{\frac{3}{2}} + 16 x ^{2}}{8} = \frac{1}{8} + \frac{8 x}{8} + \frac{24 x}{8} + \frac{32 x ^{\frac{3}{2}}}{8} + \frac{16 x ^{2}}{8}

= \frac{1}{8} + \frac{8 x}{8} + \frac{24 x}{8} + \frac{32 x ^{\frac{3}{2}}}{8} + \frac{16 x ^{2}}{8}

\frac{8 x}{8} = x

\frac{24 x}{8} = 3 x

\frac{32 x ^{\frac{3}{2}}}{8} = 4 x^{\frac{3}{2}}

\frac{16 x ^{2}}{8} = 2 x^{2}

= \frac{1}{8} + x + 3 x + 4 x^{\frac{3}{2}} + 2 x^{2}

e x p an d (- 16 e^{x} sin (x)) (8 e^{x} cos (x) - 8 e^{x} sin (x))

e x p an d \frac{π ( x ^{6} + 1 )}{3}

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

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

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