erweitern (a(a^5-ab^2+b^3))/b

Lösung

erweitern

\frac{a ( a ^{5} - a b ^{2} + b ^{3} )}{b}

\frac{a ^{6}}{b} - a^{2} b + a b^{2}

Schritte zur Lösung

\frac{a ( a ^{5} - a b ^{2} + b ^{3} )}{b}

Multipliziere aus

a (a^{5} - a b^{2} + b^{3}) : a^{6} - a^{2} b^{2} + a b^{3}

= \frac{a ^{6} - a ^{2} b ^{2} + a b ^{3}}{b}

Wende Bruchregel an:

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

\frac{a ^{6} - a ^{2} b ^{2} + a b ^{3}}{b} = \frac{a ^{6}}{b} - \frac{a ^{2} b ^{2}}{b} + \frac{a b ^{3}}{b}

= \frac{a ^{6}}{b} - \frac{a ^{2} b ^{2}}{b} + \frac{a b ^{3}}{b}

Streiche

\frac{a ^{2} b ^{2}}{b} : a^{2} b

= \frac{a ^{6}}{b} - a^{2} b + \frac{a b ^{3}}{b}

Streiche

\frac{a b ^{3}}{b} : a b^{2}

= \frac{a ^{6}}{b} - a^{2} b + a b^{2}

e x p an d \frac{s + 8}{( s + 3 ) ( s + 6 ) ( s + 10 )}

s im pl i f y (cos (x)) (1 - sin (x))

e x p an d \frac{8}{( x + 2 ) ( x - 2 )}

e x p an d (\frac{x}{4})^{2}

e x p an d e^{5 v} sin (2 (t - v))