erweitern (x(2-x)^4)/4

Lösung

erweitern

\frac{x ( 2 - x ) ^{4}}{4}

\frac{x ^{5}}{4} - 2 x^{4} + 6 x^{3} - 8 x^{2} + 4 x

Schritte zur Lösung

\frac{x ( 2 - x ) ^{4}}{4}

(2 - x)^{4} = 16 - 32 x + 24 x^{2} - 8 x^{3} + x^{4}

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

Multipliziere aus

x (16 - 32 x + 24 x^{2} - 8 x^{3} + x^{4}) : 16 x - 32 x^{2} + 24 x^{3} - 8 x^{4} + x^{5}

= \frac{16 x - 32 x ^{2} + 24 x ^{3} - 8 x ^{4} + x ^{5}}{4}

Wende Bruchregel an:

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

\frac{16 x - 32 x ^{2} + 24 x ^{3} - 8 x ^{4} + x ^{5}}{4} = \frac{16 x}{4} - \frac{32 x ^{2}}{4} + \frac{24 x ^{3}}{4} - \frac{8 x ^{4}}{4} + \frac{x ^{5}}{4}

= \frac{16 x}{4} - \frac{32 x ^{2}}{4} + \frac{24 x ^{3}}{4} - \frac{8 x ^{4}}{4} + \frac{x ^{5}}{4}

\frac{16 x}{4} = 4 x

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

\frac{24 x ^{3}}{4} = 6 x^{3}

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

= 4 x - 8 x^{2} + 6 x^{3} - 2 x^{4} + \frac{x ^{5}}{4}

Rewrite in standard form

= \frac{x ^{5}}{4} - 2 x^{4} + 6 x^{3} - 8 x^{2} + 4 x

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

e x p an d (2 x) (3 x + 1 + 1)

e x p an d (- \frac{1}{2} e^{t} + \frac{3}{2} e^{- t}) \cdot (4 e^{t} + e^{- t})

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

e x p an d sin (\frac{( 2 x - 1 ) π}{2})