erweitern (t^{1/2}+t^{1/3})^3

Lösung

erweitern

(t^{\frac{1}{2}} + t^{\frac{1}{3}})^{3}

t^{\frac{3}{2}} + 3 t^{\frac{4}{3}} + 3 t^{\frac{7}{6}} + t

Schritte zur Lösung

(t^{\frac{1}{2}} + t^{\frac{1}{3}})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(t^{\frac{1}{2}} + t^{\frac{1}{3}})^{3} = (t^{\frac{1}{2}})^{3} + 3 (t^{\frac{1}{2}})^{2} t^{\frac{1}{3}} + 3 t^{\frac{1}{2}} (t^{\frac{1}{3}})^{2} + (t^{\frac{1}{3}})^{3}

= (t^{\frac{1}{2}})^{3} + 3 (t^{\frac{1}{2}})^{2} t^{\frac{1}{3}} + 3 t^{\frac{1}{2}} (t^{\frac{1}{3}})^{2} + (t^{\frac{1}{3}})^{3}

(t^{\frac{1}{2}})^{3} = t^{\frac{3}{2}}

3 (t^{\frac{1}{2}})^{2} t^{\frac{1}{3}} = 3 t^{\frac{4}{3}}

3 t^{\frac{1}{2}} (t^{\frac{1}{3}})^{2} = 3 t^{\frac{7}{6}}

(t^{\frac{1}{3}})^{3} = t

= t^{\frac{3}{2}} + 3 t^{\frac{4}{3}} + 3 t^{\frac{7}{6}} + t

\frac{d}{d t} ((X) (2 X (N - X)))

e x p an d \frac{20}{( s ^{2} + 16 ) ( s + 7 )}

s im pl i f y (x - y) \cdot (x + y)

e x p an d - (x - 2) x

s im pl i f y x \cdot 120 (1 - \frac{x}{80}) - 2100