erweitern ((3a}{2b}+\frac{4b^2)/5)^3

Lösung

erweitern

(\frac{3 a}{2 b} + \frac{4 b ^{2}}{5})^{3}

\frac{3375 a ^{3} + 5400 a ^{2} b ^{3} + 2880 a b ^{6} + 512 b ^{9}}{1000 b ^{3}}

Schritte zur Lösung

(\frac{3 a}{2 b} + \frac{4 b ^{2}}{5})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(\frac{3 a}{2 b} + \frac{4 b ^{2}}{5})^{3} = (\frac{3 a}{2 b})^{3} + 3 (\frac{3 a}{2 b})^{2} \frac{4 b ^{2}}{5} + 3 \cdot \frac{3 a}{2 b} (\frac{4 b ^{2}}{5})^{2} + (\frac{4 b ^{2}}{5})^{3}

= (\frac{3 a}{2 b})^{3} + 3 (\frac{3 a}{2 b})^{2} \frac{4 b ^{2}}{5} + 3 \cdot \frac{3 a}{2 b} (\frac{4 b ^{2}}{5})^{2} + (\frac{4 b ^{2}}{5})^{3}

Vereinfache

(\frac{3 a}{2 b})^{3} + 3 (\frac{3 a}{2 b})^{2} \frac{4 b ^{2}}{5} + 3 \cdot \frac{3 a}{2 b} (\frac{4 b ^{2}}{5})^{2} + (\frac{4 b ^{2}}{5})^{3} : \frac{3375 a ^{3} + 5400 a ^{2} b ^{3} + 2880 a b ^{6} + 512 b ^{9}}{1000 b ^{3}}

= \frac{3375 a ^{3} + 5400 a ^{2} b ^{3} + 2880 a b ^{6} + 512 b ^{9}}{1000 b ^{3}}

e x p an d (x - \frac{2}{x})^{10}

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

e x p an d (4, 2, - 3, 5, - 1) l e f t (2, 6, - 1, - 4, 8)

s im pl i f y (2 x - 5)^{2}

e x p an d (- 1, - 5) y