faktorisieren 64t^6-1

Lösung

faktorisieren

64 t^{6} - 1

(2 t + 1) (2 t - 1) (4 t^{2} + 2 t + 1) (4 t^{2} - 2 t + 1)

Schritte zur Lösung

64 t^{6} - 1

Wende Exponentenregel an

= (4 t^{2})^{3} - 1^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(4 t^{2})^{3} - 1^{3} = (4 t^{2} - 1) (4^{2} t^{4} + 4 t^{2} + 1)

= (4 t^{2} - 1) (4^{2} t^{4} + 4 t^{2} + 1)

Faktorisiere

4 t^{2} - 1 : (2 t + 1) (2 t - 1)

= (2 t + 1) (2 t - 1) (4^{2} t^{4} + 4 t^{2} + 1)

Faktorisiere

4^{2} t^{4} + 4 t^{2} + 1 : (4 t^{2} + 1 + 2 t) (4 t^{2} + 1 - 2 t)

= (2 t + 1) (2 t - 1) (4 t^{2} + 1 + 2 t) (4 t^{2} + 1 - 2 t)

= (2 t + 1) (2 t - 1) (4 t^{2} + 2 t + 1) (4 t^{2} - 2 t + 1)

s im pl i f y 1. 4^{2}

2 k (- 3 k + 4) + 6 (k^{2} + 10) = k (4 k + 8) - 2 k (2 k + 5)

s im pl i f y (1 - i) (- 2 + i)

- 14.5 = 0.5 x - 14.5

42 + y = 86