erweitern-sin(t)(-t+sin(t))^2

Lösung

erweitern

- sin (t) (- t + sin (t))^{2}

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

Schritte zur Lösung

- sin (t) (- t + sin (t))^{2}

Schreibe

(- t + sin (t))^{2}

um:

t^{2} - 2 t sin (t) + sin^{2} (t)

= - sin (t) (t^{2} - 2 t sin (t) + sin^{2} (t))

Wende das Distributivgesetz an:

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

- sin (t) (t^{2} - 2 t sin (t) + sin^{2} (t)) = - sin (t) t^{2} - sin (t) (- 2 t sin (t)) - sin (t) sin^{2} (t)

= - sin (t) t^{2} - sin (t) (- 2 t sin (t)) - sin (t) sin^{2} (t)

Vereinfache

- sin (t) t^{2} - sin (t) (- 2 t sin (t)) - sin (t) sin^{2} (t) : - t^{2} sin (t) + 2 t sin^{2} (t) - sin^{3} (t)

= - t^{2} sin (t) + 2 t sin^{2} (t) - sin^{3} (t)

e x p an d \frac{10 ( h + 3 )}{h - 3}

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

e x p an d x (v^{2} - 1) d v + v^{3} - 3 v

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

e x p an d (a + b x + c x^{2}) \cdot (d + e x + f x^{2})