erweitern (4(x+h)^2)/h

Lösung

erweitern

\frac{4 ( x + h ) ^{2}}{h}

\frac{4 x ^{2}}{h} + 8 x + 4 h

Schritte zur Lösung

\frac{4 ( x + h ) ^{2}}{h}

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

= \frac{4 ( x ^{2} + 2 x h + h ^{2} )}{h}

Multipliziere aus

4 (x^{2} + 2 x h + h^{2}) : 4 x^{2} + 8 x h + 4 h^{2}

= \frac{4 x ^{2} + 8 x h + 4 h ^{2}}{h}

Wende Bruchregel an:

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

\frac{4 x ^{2} + 8 x h + 4 h ^{2}}{h} = \frac{4 x ^{2}}{h} + \frac{8 x h}{h} + \frac{4 h ^{2}}{h}

= \frac{4 x ^{2}}{h} + \frac{8 x h}{h} + \frac{4 h ^{2}}{h}

Streiche

\frac{8 x h}{h} : 8 x

= \frac{4 x ^{2}}{h} + 8 x + \frac{4 h ^{2}}{h}

Streiche

\frac{4 h ^{2}}{h} : 4 h

= \frac{4 x ^{2}}{h} + 8 x + 4 h

e x p an d (2 - 3 a b^{2})^{14}

e x p an d \frac{x + 13}{( x + 1 ) ( x - 10 )}

e x p an d \frac{2 x ^{2}}{( x - 3 ) ( x + 5 )}

e x p an d \frac{2 ( x + 9 )}{5}

e x p an d (sin (x) + e^{x})^{2}