erweitern ((x+h)^2-x^3)/h

Lösung

erweitern

\frac{( x + h ) ^{2} - x ^{3}}{h}

\frac{x ^{2}}{h} + 2 x + h - \frac{x ^{3}}{h}

Schritte zur Lösung

\frac{( x + h ) ^{2} - x ^{3}}{h}

Multipliziere aus

(x + h)^{2} - x^{3} : x^{2} + 2 x h + h^{2} - x^{3}

= \frac{x ^{2} + 2 x h + h ^{2} - x ^{3}}{h}

Wende Bruchregel an:

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

\frac{x ^{2} + 2 x h + h ^{2} - x ^{3}}{h} = \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} - \frac{x ^{3}}{h}

= \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} - \frac{x ^{3}}{h}

Streiche

\frac{2 x h}{h} : 2 x

= \frac{x ^{2}}{h} + 2 x + \frac{h ^{2}}{h} - \frac{x ^{3}}{h}

Streiche

\frac{h ^{2}}{h} : h

= \frac{x ^{2}}{h} + 2 x + h - \frac{x ^{3}}{h}

e x p an d (m + 3, n - 5) (11 - m, m)

e x p an d (x - 3)^{17}

e x p an d \frac{d}{d x} ((3 x - 2) (x + 3)) - 4 x

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

e x p an d \frac{3 x - 4}{x ^{2} ( x + 2 )}