erweitern (cos(t)+5e^{4t})^3

Lösung

erweitern

(cos (t) + 5 e^{4 t})^{3}

cos^{3} (t) + 15 e^{4 t} cos^{2} (t) + 75 e^{8 t} cos (t) + 125 e^{12 t}

Schritte zur Lösung

(cos (t) + 5 e^{4 t})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

a = cos (t), b = 5 e^{4 t}

= cos^{3} (t) + 3 cos^{2} (t) \cdot 5 e^{4 t} + 3 cos (t) (5 e^{4 t})^{2} + (5 e^{4 t})^{3}

Vereinfache

cos^{3} (t) + 3 cos^{2} (t) \cdot 5 e^{4 t} + 3 cos (t) (5 e^{4 t})^{2} + (5 e^{4 t})^{3} : cos^{3} (t) + 15 e^{4 t} cos^{2} (t) + 75 e^{8 t} cos (t) + 125 e^{12 t}

= cos^{3} (t) + 15 e^{4 t} cos^{2} (t) + 75 e^{8 t} cos (t) + 125 e^{12 t}

s im pl i f y (x + 25)^{2}

s im pl i f y (cos (x) + i sin (x))^{3}

e x p an d (- 5, 8) y (- 5, - 6)

e x p an d (csc (x) + 1) tan (x) - sec (x)

s im pl i f y (1 + i)^{9}