erweitern (2c^2+d^2)^3

Lösung

erweitern

(2 c^{2} + d^{2})^{3}

8 c^{6} + 12 c^{4} d^{2} + 6 c^{2} d^{4} + d^{6}

Schritte zur Lösung

(2 c^{2} + d^{2})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(2 c^{2} + d^{2})^{3} = (2 c^{2})^{3} + 3 (2 c^{2})^{2} d^{2} + 3 \cdot 2 c^{2} (d^{2})^{2} + (d^{2})^{3}

= (2 c^{2})^{3} + 3 (2 c^{2})^{2} d^{2} + 3 \cdot 2 c^{2} (d^{2})^{2} + (d^{2})^{3}

Vereinfache

(2 c^{2})^{3} + 3 (2 c^{2})^{2} d^{2} + 3 \cdot 2 c^{2} (d^{2})^{2} + (d^{2})^{3} : 8 c^{6} + 12 c^{4} d^{2} + 6 c^{2} d^{4} + d^{6}

= 8 c^{6} + 12 c^{4} d^{2} + 6 c^{2} d^{4} + d^{6}

s im pl i f y (1 + i) (x + i y)

s im pl i f y \frac{4}{4 - 3}

s im pl i f y \frac{72}{110}

f a c t or a^{2} - 6 a b^{2} + 9 b^{4}

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