erweitern (sin(x)+1)(sin(x)-1)(4sin(x)+1)

Lösung

erweitern

(sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1)

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

Schritte zur Lösung

(sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1)

Schreibe

(sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1)

um:

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

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

Wende das Distributivgesetz an:

a (b + c) = ab + a c

- cos^{2} (x) (4 sin (x) + 1) = - cos^{2} (x) \cdot 4 sin (x) - cos^{2} (x) \cdot 1

= - cos^{2} (x) \cdot 4 sin (x) - cos^{2} (x) \cdot 1

Vereinfache

- cos^{2} (x) \cdot 4 sin (x) - cos^{2} (x) \cdot 1 : - 4 cos^{2} (x) sin (x) - cos^{2} (x)

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

e x p an d - 6 (e^{x} - e^{2 x})

e x p an d x^{\frac{4}{5}} \times (x - 4)^{2}

e x p an d \frac{e ^{- t} t ^{2} ( 14 + 2 t )}{9} + 15 - 10 t

s im pl i f y (\frac{3 x ^{3}}{2} + 9 y^{2}) (\frac{3 x ^{3}}{2} - 9 y^{2})

e x p an d (x + 1) (x - 4) (x - 2)