erweitern ((x^2+5)^3)/6

Lösung

erweitern

\frac{( x ^{2} + 5 ) ^{3}}{6}

\frac{x ^{6}}{6} + \frac{5 x ^{4}}{2} + \frac{25 x ^{2}}{2} + \frac{125}{6}

Schritte zur Lösung

\frac{( x ^{2} + 5 ) ^{3}}{6}

(x^{2} + 5)^{3} = x^{6} + 15 x^{4} + 75 x^{2} + 125

= \frac{x ^{6} + 15 x ^{4} + 75 x ^{2} + 125}{6}

Wende Bruchregel an:

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

\frac{x ^{6} + 15 x ^{4} + 75 x ^{2} + 125}{6} = \frac{x ^{6}}{6} + \frac{15 x ^{4}}{6} + \frac{75 x ^{2}}{6} + \frac{125}{6}

= \frac{x ^{6}}{6} + \frac{15 x ^{4}}{6} + \frac{75 x ^{2}}{6} + \frac{125}{6}

Streiche

\frac{15 x ^{4}}{6} : \frac{5 x ^{4}}{2}

= \frac{x ^{6}}{6} + \frac{5 x ^{4}}{2} + \frac{75 x ^{2}}{6} + \frac{125}{6}

Streiche

\frac{75 x ^{2}}{6} : \frac{25 x ^{2}}{2}

= \frac{x ^{6}}{6} + \frac{5 x ^{4}}{2} + \frac{25 x ^{2}}{2} + \frac{125}{6}

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

e x p an d x d y \cdot (y + 3) - d y (y + 3)

\frac{d}{d t} ((s) (6 t^{5} - 8 t + 5))

e x p an d (a, b) - 12 (a - b)^{2} + 7 (a - b) - 12

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