erweitern-(-3+sin^2(x))^2cos(x)sin(x)

Lösung

erweitern

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

- 9 cos (x) sin (x) + 6 sin^{3} (x) cos (x) - sin^{5} (x) cos (x)

Schritte zur Lösung

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

= - cos (x) sin (x) (- 3 + sin^{2} (x))^{2}

Schreibe

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

um:

9 - 6 sin^{2} (x) + sin^{4} (x)

= - cos (x) sin (x) (9 - 6 sin^{2} (x) + sin^{4} (x))

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

- cos (x) sin (x) (9 - 6 sin^{2} (x) + sin^{4} (x)) = - cos (x) sin (x) \cdot 9 - cos (x) sin (x) (- 6 sin^{2} (x)) - cos (x) sin (x) sin^{4} (x)

= - cos (x) sin (x) \cdot 9 - cos (x) sin (x) (- 6 sin^{2} (x)) - cos (x) sin (x) sin^{4} (x)

Vereinfache

- cos (x) sin (x) \cdot 9 - cos (x) sin (x) (- 6 sin^{2} (x)) - cos (x) sin (x) sin^{4} (x) : - 9 cos (x) sin (x) + 6 sin^{3} (x) cos (x) - sin^{5} (x) cos (x)

= - 9 cos (x) sin (x) + 6 sin^{3} (x) cos (x) - sin^{5} (x) cos (x)

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

e x p an d (2 - \frac{x}{2})^{10}

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

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

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