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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

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

Entferne die Klammern:

(a) = a, - (- a) = a

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

Teile die Zahlen:

\frac{4}{4} = 1

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

Streiche

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

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

Teile die Zahlen:

\frac{4}{4} = 1

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

Rewrite in standard form

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

e x p an d 12 (- \frac{195}{16} + \frac{49}{2} ln (14))

e x p an d \frac{14 ( e ^{6} - 1 )}{12}

e x p an d A (B x + Ct + D)^{2}

e x p an d (x + 5) e^{2 x}

e x p an d \frac{\frac{d}{d x} ( x ^{3} + 3 )}{( x + 5 ) ^{2}}