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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

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

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

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

Vereinfache

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

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

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

s im pl i f y (z - 6 i)^{2}

e x p an d \frac{( x - 6 ) ^{4}}{81}

e x p an d 6 (- 1)^{5} - 24 (- 1)^{3} + 18 (- 1)

e x p an d \frac{2 ( - 24 s - 6 s ^{2} + 12 )}{s ( - s ^{2} - 3 s + 6 )}