erweitern (cos^2(x)-2sin(x))^2

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

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

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

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

Vereinfache

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

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

e x p an d (12) (8) (- 8) (- 12)

e x p an d \frac{( 2 x + y ^{3} ) ^{2}}{x ^{2} + y ^{4}}

s im pl i f y x^{\frac{3}{2}} - 4 x (x + 4)

e x p an d 2 (e^{4} - e^{2}) - 12

s im pl i f y t (x) x^{^{''}} - (t (x) + 2) x^{^{'}} + 2 x