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Beliebt Algebra >

erweitern (-e^tsin(t)+e^tcos(t))(2e^tcos(t))

Lösung

erweitern

(- e^{t} sin (t) + e^{t} cos (t)) (2 e^{t} cos (t))

Lösung

- 2 e^{2 t} sin (t) cos (t) + 2 e^{2 t} cos^{2} (t)

Schritte zur Lösung

(- e^{t} sin (t) + e^{t} cos (t)) (2 e^{t} cos (t))

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = (2 e^{t} cos (t)), b = - e^{t} sin (t), c = e^{t} cos (t)

= (2 e^{t} cos (t)) (- e^{t} sin (t)) + (2 e^{t} cos (t)) e^{t} cos (t)

Wende Minus-Plus Regeln an

+ (- a) = - a

= - e^{t} sin (t) (2 e^{t} cos (t)) + e^{t} cos (t) (2 e^{t} cos (t))

Vereinfache

- e^{t} sin (t) (2 e^{t} cos (t)) + e^{t} cos (t) (2 e^{t} cos (t)) : - 2 e^{2 t} sin (t) cos (t) + 2 e^{2 t} cos^{2} (t)

= - 2 e^{2 t} sin (t) cos (t) + 2 e^{2 t} cos^{2} (t)

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