erweitern (x+x*i)^3-2i

Lösung

erweitern

(x + x \cdot i)^{3} - 2 i

- 2 x^{3} + (2 x^{3} - 2) i

Schritte zur Lösung

(x + x i)^{3} - 2 i

Wende Formel für perfekte dritte Potenzen an:

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

(x + x i)^{3} = x^{3} + 3 x^{2} x i + 3 x (x i)^{2} + (x i)^{3}

= x^{3} + 3 x^{2} x i + 3 x (x i)^{2} + (x i)^{3} - 2 i

Vereinfache

x^{3} + 3 x^{2} x i + 3 x (x i)^{2} + (x i)^{3} : - 2 x^{3} + 2 x^{3} i

= - 2 x^{3} + 2 x^{3} i - 2 i

Rewrite in standard complex form:

- 2 x^{3} + (2 x^{3} - 2) i

= - 2 x^{3} + (2 x^{3} - 2) i

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

s im pl i f y 10 (4 lo g_{2} (40) + 48 lo g_{2} (1300))

e x p an d \frac{9}{( x + 5 ) ^{2}}

s im pl i f y (P + \frac{a}{V ^{2}}) (V - b) - RT

e x p an d \frac{2 x + 2 h}{x ^{2} + 2 x h + h ^{2} + 1} - \frac{2 x}{x ^{2} + 1}