展開する (e^tcos(t)-e^tsin(t))(2e^tcos(t))

解

展開する

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

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

解答ステップ

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

分配法則を適用する:

a (b - c) = ab - a c

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

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

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

簡素化

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