erweitern ((-x+1)^4)/4

Lösung

erweitern

\frac{( - x + 1 ) ^{4}}{4}

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

Schritte zur Lösung

\frac{( - x + 1 ) ^{4}}{4}

(- x + 1)^{4} = x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1

= \frac{x ^{4} - 4 x ^{3} + 6 x ^{2} - 4 x + 1}{4}

Wende Bruchregel an:

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

\frac{x ^{4} - 4 x ^{3} + 6 x ^{2} - 4 x + 1}{4} = \frac{x ^{4}}{4} - \frac{4 x ^{3}}{4} + \frac{6 x ^{2}}{4} - \frac{4 x}{4} + \frac{1}{4}

= \frac{x ^{4}}{4} - \frac{4 x ^{3}}{4} + \frac{6 x ^{2}}{4} - \frac{4 x}{4} + \frac{1}{4}

Teile die Zahlen:

\frac{4}{4} = 1

= \frac{x ^{4}}{4} - x^{3} + \frac{6 x ^{2}}{4} - \frac{4 x}{4} + \frac{1}{4}

Streiche

\frac{6 x ^{2}}{4} : \frac{3 x ^{2}}{2}

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

Teile die Zahlen:

\frac{4}{4} = 1

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

e x p an d (9 x + 45 x^{2} + 98 7^{3})^{5}

e x p an d (x - y = arcsin (x) - arcsin (y)) \frac{d y}{d x}

e x p an d \frac{8}{s ( 2 s ^{2} + 4 s + 3 )}

e x p an d (π + 1)^{2}

e x p an d \frac{s + 1500}{s ( s + 200 )}