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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

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

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

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

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

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

s im pl i f y (x - 1 + i 2)^{2} \cdot (x + 1 + i 2)^{2}

e x p an d (x - 5) (x + 5)

e x p an d x^{2} (1 + 1 - x^{2})

e x p an d \frac{( 3 x ^{4} )}{( 8 x ^{5} - 3 ) ^{4}}