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

Lösung

erweitern

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

\frac{3 x ^{2}}{h} + 6 x + 3 h - \frac{3 x}{h}

Schritte zur Lösung

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

(x + h)^{2} = x^{2} + 2 x h + h^{2}

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

Multipliziere aus

3 (x^{2} + 2 x h + h^{2}) - 3 x : 3 x^{2} + 6 x h + 3 h^{2} - 3 x

= \frac{3 x ^{2} + 6 x h + 3 h ^{2} - 3 x}{h}

Wende Bruchregel an:

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

\frac{3 x ^{2} + 6 x h + 3 h ^{2} - 3 x}{h} = \frac{3 x ^{2}}{h} + \frac{6 x h}{h} + \frac{3 h ^{2}}{h} - \frac{3 x}{h}

= \frac{3 x ^{2}}{h} + \frac{6 x h}{h} + \frac{3 h ^{2}}{h} - \frac{3 x}{h}

Streiche

\frac{6 x h}{h} : 6 x

= \frac{3 x ^{2}}{h} + 6 x + \frac{3 h ^{2}}{h} - \frac{3 x}{h}

Streiche

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

= \frac{3 x ^{2}}{h} + 6 x + 3 h - \frac{3 x}{h}

e x p an d d y - (y - 8)^{2} d x

e x p an d (x + 3) (x + 4 = 0)

e x p an d \frac{9}{( 3 x - 1 ) ( 3 x + 5 )}

e x p an d ln (x) (6 x + 1)

e x p an d \frac{b ( 1 + 1.1 r )}{1 - 1.1 r}