erweitern (2-2/3 z)^3

Lösung

erweitern

(2 - \frac{2}{3} z)^{3}

\frac{216 - 216 z + 72 z ^{2} - 8 z ^{3}}{27}

Schritte zur Lösung

(2 - \frac{2}{3} z)^{3}

Wende Formel für perfekte dritte Potenzen an:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(2 - \frac{2}{3} z)^{3} = 2^{3} - 3 \cdot 2^{2} \cdot \frac{2}{3} z + 3 \cdot 2 (\frac{2}{3} z)^{2} - (\frac{2}{3} z)^{3}

= 2^{3} - 3 \cdot 2^{2} \cdot \frac{2}{3} z + 3 \cdot 2 (\frac{2}{3} z)^{2} - (\frac{2}{3} z)^{3}

Vereinfache

2^{3} - 3 \cdot 2^{2} \cdot \frac{2}{3} z + 3 \cdot 2 (\frac{2}{3} z)^{2} - (\frac{2}{3} z)^{3} : \frac{216 - 216 z + 72 z ^{2} - 8 z ^{3}}{27}

= \frac{216 - 216 z + 72 z ^{2} - 8 z ^{3}}{27}

\frac{\partial}{\partial y} ((z) (8 x yz - e^{z}))

e x p an d - \frac{1}{( 3 - x ) ^{2} ( 1 - x )}

e x p an d \frac{4 ( - 2 x ^{2} + 24 x )}{( 7 x ^{2} - 2 x + 12 ) ^{2}}

e x p an d (x - 16) x

e x p an d (\frac{7 - 3 x}{4})^{2}