erweitern fcos(x)(1+5sin(x))^3

Lösung

erweitern

f cos (x) (1 + 5 sin (x))^{3}

f cos (x) + 15 f cos (x) sin (x) + 75 f sin^{2} (x) cos (x) + 125 f sin^{3} (x) cos (x)

Schritte zur Lösung

f cos (x) (1 + 5 sin (x))^{3}

Schreibe

(1 + 5 sin (x))^{3}

um:

1 + 15 sin (x) + 75 sin^{2} (x) + 125 sin^{3} (x)

= f cos (x) (1 + 15 sin (x) + 75 sin^{2} (x) + 125 sin^{3} (x))

Setze Klammern

= f cos (x) \cdot 1 + f cos (x) \cdot 15 sin (x) + f cos (x) \cdot 75 sin^{2} (x) + f cos (x) \cdot 125 sin^{3} (x)

Vereinfache

f cos (x) \cdot 1 + f cos (x) \cdot 15 sin (x) + f cos (x) \cdot 75 sin^{2} (x) + f cos (x) \cdot 125 sin^{3} (x) : f cos (x) + 15 f cos (x) sin (x) + 75 f sin^{2} (x) cos (x) + 125 f sin^{3} (x) cos (x)

= f cos (x) + 15 f cos (x) sin (x) + 75 f sin^{2} (x) cos (x) + 125 f sin^{3} (x) cos (x)

s im pl i f y (33 - x)^{2}

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

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

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

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