faktorisieren t^6-64

Lösung

faktorisieren

t^{6} - 64

(t + 2) (t - 2) (t^{2} + 2 t + 4) (t^{2} - 2 t + 4)

Schritte zur Lösung

t^{6} - 64

Wende Exponentenregel an

= (t^{2})^{3} - 4^{3}

Wende Formel zur Differenz von dritten Potenzen an:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(t^{2})^{3} - 4^{3} = (t^{2} - 4) (t^{4} + 4 t^{2} + 4^{2})

= (t^{2} - 4) (t^{4} + 4 t^{2} + 4^{2})

Faktorisiere

t^{2} - 4 : (t + 2) (t - 2)

= (t + 2) (t - 2) (t^{4} + 4 t^{2} + 4^{2})

Faktorisiere

t^{4} + 4 t^{2} + 4^{2} : (t^{2} + 4 + 2 t) (t^{2} + 4 - 2 t)

= (t + 2) (t - 2) (t^{2} + 4 + 2 t) (t^{2} + 4 - 2 t)

= (t + 2) (t - 2) (t^{2} + 2 t + 4) (t^{2} - 2 t + 4)

\frac{1}{2} (8 - x) = 8 - \frac{x}{2}

x^{2} - \frac{x}{2} = \frac{1}{3} - \frac{2 x}{3}

0.5 x^{2} + x = 0

45 x + 2 = 180

- 5 x - 5 < - 4 x - 4