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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Entferne die Klammern:

(a) = a

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Streiche

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

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

e x p an d \frac{a}{( a + b ) ^{2}}

e x p an d \frac{6 x ^{3}}{( x - 7 ) ^{2}}

e x p an d 7 (3 x + 4 y = - 20)

e x p an d x^{'} z (x) + y (x, z (x)) (x + z (x))

e x p an d 25 (33 - π)