erweitern ((a^2-b^2)(b+a))/b

Lösung

erweitern

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

a^{2} + \frac{a ^{3}}{b} - b^{2} - ab

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Streiche

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

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

Streiche

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

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

Streiche

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

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

e x p an d sin^{2} (π (x + 1)^{3})

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

e x p an d (x^{2} + 3 x + 5)^{8} d x

e x p an d 524 - 4^{2}

e x p an d (e - 2 f)^{3}