erweitern (((n-1)(n^3-n^2-14n+12)))/(12)

Lösung

erweitern

\frac{( ( n - 1 ) \cdot ( n ^{3} - n ^{2} - 14 \cdot n + 12 ) )}{12}

\frac{n ^{4}}{12} - \frac{n ^{3}}{6} - \frac{13 n ^{2}}{12} + \frac{13 n}{6} - 1

Schritte zur Lösung

\frac{( n - 1 ) ( n ^{3} - n ^{2} - 14 n + 12 )}{12}

Multipliziere aus

(n - 1) (n^{3} - n^{2} - 14 n + 12) : n^{4} - 2 n^{3} - 13 n^{2} + 26 n - 12

= \frac{n ^{4} - 2 n ^{3} - 13 n ^{2} + 26 n - 12}{12}

Wende Bruchregel an:

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

\frac{n ^{4} - 2 n ^{3} - 13 n ^{2} + 26 n - 12}{12} = \frac{n ^{4}}{12} - \frac{2 n ^{3}}{12} - \frac{13 n ^{2}}{12} + \frac{26 n}{12} - \frac{12}{12}

= \frac{n ^{4}}{12} - \frac{2 n ^{3}}{12} - \frac{13 n ^{2}}{12} + \frac{26 n}{12} - \frac{12}{12}

Wende Regel an

\frac{a}{a} = 1

\frac{12}{12} = 1

= \frac{n ^{4}}{12} - \frac{2 n ^{3}}{12} - \frac{13 n ^{2}}{12} + \frac{26 n}{12} - 1

Streiche

\frac{2 n ^{3}}{12} : \frac{n ^{3}}{6}

= \frac{n ^{4}}{12} - \frac{n ^{3}}{6} - \frac{13 n ^{2}}{12} + \frac{26 n}{12} - 1

Streiche

\frac{26 n}{12} : \frac{13 n}{6}

= \frac{n ^{4}}{12} - \frac{n ^{3}}{6} - \frac{13 n ^{2}}{12} + \frac{13 n}{6} - 1

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

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

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

e x p an d (x^{2} - 5) (x + 6)^{'}

e x p an d (x + y + z) (x + y + z)