faktorisieren x^6-27x^4+243x^2-729

Lösung

faktorisieren

x^{6} - 27 x^{4} + 243 x^{2} - 729

(x + 3)^{3} (x - 3)^{3}

Schritte zur Lösung

x^{6} - 27 x^{4} + 243 x^{2} - 729

Angenommen

u = x^{2}

= u^{3} - 27 u^{2} + 243 u - 729

Faktorisiere

u^{3} - 27 u^{2} + 243 u - 729 : (u - 9) (u - 9) (u - 9)

= (u - 9) (u - 9) (u - 9)

Setze in

u = x^{2}

ein

= (x^{2} - 9) (x^{2} - 9) (x^{2} - 9)

Faktorisiere

x^{2} - 9 : (x + 3) (x - 3)

= (x + 3) (x - 3) (x^{2} - 9) (x^{2} - 9)

Faktorisiere

x^{2} - 9 : (x + 3) (x - 3)

= (x + 3) (x - 3) (x + 3) (x - 3) (x^{2} - 9)

Faktorisiere

x^{2} - 9 : (x + 3) (x - 3)

= (x + 3) (x - 3) (x + 3) (x - 3) (x + 3) (x - 3)

Fasse zusammen

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

f a c t or 3 (r - 2)^{2} - 7 (r - 2) + 2

f a c t or 10 x - 10 y - x^{5} + x^{4} y

f a c t or 64 + (3 x + 2)^{3}

f a c t or m^{3} n^{3} x^{3} + 1

f a c t or 1 - 2 cos (2 x) + cos^{2} (2 x)