erweitern ((a+h)^3)/h

Lösung

erweitern

\frac{( a + h ) ^{3}}{h}

\frac{a ^{3}}{h} + 3 a^{2} + 3 ah + h^{2}

Schritte zur Lösung

\frac{( a + h ) ^{3}}{h}

(a + h)^{3} = a^{3} + 3 a^{2} h + 3 a h^{2} + h^{3}

= \frac{a ^{3} + 3 a ^{2} h + 3 a h ^{2} + h ^{3}}{h}

Wende Bruchregel an:

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

\frac{a ^{3} + 3 a ^{2} h + 3 a h ^{2} + h ^{3}}{h} = \frac{a ^{3}}{h} + \frac{3 a ^{2} h}{h} + \frac{3 a h ^{2}}{h} + \frac{h ^{3}}{h}

= \frac{a ^{3}}{h} + \frac{3 a ^{2} h}{h} + \frac{3 a h ^{2}}{h} + \frac{h ^{3}}{h}

Streiche

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

= \frac{a ^{3}}{h} + 3 a^{2} + \frac{3 a h ^{2}}{h} + \frac{h ^{3}}{h}

Streiche

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

= \frac{a ^{3}}{h} + 3 a^{2} + 3 ah + \frac{h ^{3}}{h}

Streiche

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

= \frac{a ^{3}}{h} + 3 a^{2} + 3 ah + h^{2}

e x p an d \frac{5 ( y + 3 )}{3}

e x p an d (4 a - b) e^{3}

e x p an d P (- 9, - 4) Q (- 4, - 5)

e x p an d 7.9 \cdot 1 0^{8}

e x p an d e^{3 - 1} (6 - 23)