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Beliebt Algebra >

faktorisieren (x-1)^{7/2}-(x-1)^{3/2}

Lösung

faktorisieren

(x - 1)^{\frac{7}{2}} - (x - 1)^{\frac{3}{2}}

Lösung

x (x - 1 + 1) (x - 1 - 1) (x - 1)^{\frac{3}{2}}

Schritte zur Lösung

(x - 1)^{\frac{7}{2}} - (x - 1)^{\frac{3}{2}}

Schreibe

(x - 1)^{\frac{7}{2}}

um:

(x - 1)^{7}

= (x - 1)^{7} - (x - 1)^{\frac{3}{2}}

Schreibe

(x - 1)^{\frac{3}{2}}

um:

(x - 1)^{3}

= (x - 1)^{7} - (x - 1)^{3}

Klammere gleiche Terme aus

(x - 1)^{3} : (x - 1)^{3} ((x - 1)^{4} - 1)

= (x - 1)^{3} ((x - 1)^{4} - 1)

Faktorisiere

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

= (x - 1)^{3} ((x - 1)^{2} + 1) (x - 1 + 1) (x - 1 - 1)

Vereinfache

(x - 1)^{3} ((x - 1)^{2} + 1) (x - 1 + 1) (x - 1 - 1) : x (x - 1)^{3} (x - 1 + 1) (x - 1 - 1)

= x (x - 1)^{3} (x - 1 + 1) (x - 1 - 1)

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

= x (x - 1 + 1) (x - 1 - 1) (x - 1)^{\frac{3}{2}}

Beliebte Beispiele

∣ x - 9 ∣ = 9

x^{2} + 11 x + 28 \leq 0

2x+42+x-7+x-7=180

2 x + 42 + x - 7 + x - 7 = 180

2 x^{2} + 5 x = 3

faktorisieren x^3-8x^2+5x+14

f a c t or x^{3} - 8 x^{2} + 5 x + 14