erweitern (x^{3/2}-4)^3

Lösung

erweitern

(x^{\frac{3}{2}} - 4)^{3}

x^{\frac{9}{2}} - 12 x^{3} + 48 x^{\frac{3}{2}} - 64

Schritte zur Lösung

(x^{\frac{3}{2}} - 4)^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(x^{\frac{3}{2}} - 4)^{3} = (x^{\frac{3}{2}})^{3} - 3 (x^{\frac{3}{2}})^{2} \cdot 4 + 3 x^{\frac{3}{2}} \cdot 4^{2} - 4^{3}

= (x^{\frac{3}{2}})^{3} - 3 (x^{\frac{3}{2}})^{2} \cdot 4 + 3 x^{\frac{3}{2}} \cdot 4^{2} - 4^{3}

(x^{\frac{3}{2}})^{3} = x^{\frac{9}{2}}

3 (x^{\frac{3}{2}})^{2} \cdot 4 = 12 x^{3}

3 x^{\frac{3}{2}} \cdot 4^{2} = 48 x^{\frac{3}{2}}

4^{3} = 64

= x^{\frac{9}{2}} - 12 x^{3} + 48 x^{\frac{3}{2}} - 64

e x p an d 2 (ln (- 1) + 1)

e x p an d (5 + 11 x) x^{4} e^{11 x} + 3

e x p an d (3, 1) y (4, - 11)

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

e x p an d \frac{a}{s ( s ^{2} + a ^{2} )}