erweitern (3e^2+4d^2)^3

Lösung

erweitern

(3 e^{2} + 4 d^{2})^{3}

64 d^{6} + 144 e^{2} d^{4} + 108 e^{4} d^{2} + 27 e^{6}

Schritte zur Lösung

(3 e^{2} + 4 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}

a = 3 e^{2}, b = 4 d^{2}

= (3 e^{2})^{3} + 3 (3 e^{2})^{2} \cdot 4 d^{2} + 3 \cdot 3 e^{2} (4 d^{2})^{2} + (4 d^{2})^{3}

Vereinfache

(3 e^{2})^{3} + 3 (3 e^{2})^{2} \cdot 4 d^{2} + 3 \cdot 3 e^{2} (4 d^{2})^{2} + (4 d^{2})^{3} : 27 e^{6} + 108 e^{4} d^{2} + 144 e^{2} d^{4} + 64 d^{6}

= 27 e^{6} + 108 e^{4} d^{2} + 144 e^{2} d^{4} + 64 d^{6}

Rewrite in standard form

= 64 d^{6} + 144 e^{2} d^{4} + 108 e^{4} d^{2} + 27 e^{6}

e x p an d \frac{x ^{15}}{( x ^{8} + 1 ) ^{2}}

e x p an d x (x^{4} e^{9 x} + 3)

e x p an d x^{2} (- 5, - 1)

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

e x p an d 285.2