erweitern-(x(x-1)(x-2)(x-4))/8

Lösung

erweitern

- \frac{x ( x - 1 ) ( x - 2 ) ( x - 4 )}{8}

- \frac{x ^{4}}{8} + \frac{7 x ^{3}}{8} - \frac{7 x ^{2}}{4} + x

Schritte zur Lösung

- \frac{x ( x - 1 ) ( x - 2 ) ( x - 4 )}{8}

Multipliziere aus

x (x - 1) (x - 2) (x - 4) : x^{4} - 7 x^{3} + 14 x^{2} - 8 x

= - \frac{x ^{4} - 7 x ^{3} + 14 x ^{2} - 8 x}{8}

Wende Bruchregel an:

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

\frac{x ^{4} - 7 x ^{3} + 14 x ^{2} - 8 x}{8} = - (\frac{x ^{4}}{8}) - (- \frac{7 x ^{3}}{8}) - (\frac{14 x ^{2}}{8}) - (- \frac{8 x}{8})

= - (\frac{x ^{4}}{8}) - (- \frac{7 x ^{3}}{8}) - (\frac{14 x ^{2}}{8}) - (- \frac{8 x}{8})

Entferne die Klammern:

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

= - \frac{x ^{4}}{8} + \frac{7 x ^{3}}{8} - \frac{14 x ^{2}}{8} + \frac{8 x}{8}

Streiche

\frac{14 x ^{2}}{8} : \frac{7 x ^{2}}{4}

= - \frac{x ^{4}}{8} + \frac{7 x ^{3}}{8} - \frac{7 x ^{2}}{4} + \frac{8 x}{8}

Teile die Zahlen:

\frac{8}{8} = 1

= - \frac{x ^{4}}{8} + \frac{7 x ^{3}}{8} - \frac{7 x ^{2}}{4} + x

e x p an d x^{2} x^{3}

e x p an d (n^{7})^{2} - n^{2}

e x p an d \frac{25}{( x + 2 ) ^{2}}

e x p an d (5 x + 4 y = 2,) (3 x + 3 y = - 3)

e x p an d \frac{7 x}{( x - 7 ) ^{2}}