erweitern (1-sin^2(x))^3

Lösung

erweitern

(1 - sin^{2} (x))^{3}

1 - 3 sin^{2} (x) + 3 sin^{4} (x) - sin^{6} (x)

Schritte zur Lösung

(1 - sin^{2} (x))^{3}

Wende Formel für perfekte dritte Potenzen an:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(1 - sin^{2} (x))^{3} = 1^{3} - 3 \cdot 1^{2} sin^{2} (x) + 3 \cdot 1 \cdot (sin^{2} (x))^{2} - (sin^{2} (x))^{3}

= 1^{3} - 3 \cdot 1^{2} sin^{2} (x) + 3 \cdot 1 \cdot (sin^{2} (x))^{2} - (sin^{2} (x))^{3}

Vereinfache

1^{3} - 3 \cdot 1^{2} sin^{2} (x) + 3 \cdot 1 \cdot (sin^{2} (x))^{2} - (sin^{2} (x))^{3} : 1 - 3 sin^{2} (x) + 3 sin^{4} (x) - sin^{6} (x)

= 1 - 3 sin^{2} (x) + 3 sin^{4} (x) - sin^{6} (x)

e x p an d 2^{(x - 1)^{2}}

e x p an d \frac{2 cos ( x )}{( 1 - sin ( x ) ) ^{2}}

e x p an d ln (\frac{x - 73}{x})

e x p an d \frac{( n ) ( n + 1 ) ( 2 n + 1 )}{6}

s im pl i f y (x + 3 + 6) (x + 3 - 6)