erweitern (2e^{2x}cos(x)-e^{2x}sin(x))^2

Lösung

erweitern

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

4 e^{4 x} cos^{2} (x) - 4 e^{4 x} cos (x) sin (x) + e^{4 x} sin^{2} (x)

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

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

= (2 e^{2 x} cos (x))^{2} - 2 \cdot 2 e^{2 x} cos (x) e^{2 x} sin (x) + (e^{2 x} sin (x))^{2}

Vereinfache

(2 e^{2 x} cos (x))^{2} - 2 \cdot 2 e^{2 x} cos (x) e^{2 x} sin (x) + (e^{2 x} sin (x))^{2} : 4 e^{4 x} cos^{2} (x) - 4 e^{4 x} cos (x) sin (x) + e^{4 x} sin^{2} (x)

= 4 e^{4 x} cos^{2} (x) - 4 e^{4 x} cos (x) sin (x) + e^{4 x} sin^{2} (x)

e x p an d 30 (22 x - 18 y = 4)

e x p an d (16 e^{x} cos (x)) (8 e^{x} sin (x) + 8 e^{x} cos (x))

e x p an d \frac{( ( 224 + 2 x ) ^{2} )}{( 0.00623 - x ) ( 0.00414 - x )}

e x p an d \frac{( 2 + 3 ) ( 5 - 1 )}{2}

e x p an d \frac{1}{y ( a - b y )}