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Beliebt Algebra >

faktorisieren (x-4)^{7/2}-16(x-4)^{3/2}

Lösung

faktorisieren

(x - 4)^{\frac{7}{2}} - 16 (x - 4)^{\frac{3}{2}}

Lösung

x (x - 4 + 2) (x - 4 - 2) (x - 4)^{\frac{3}{2}}

Schritte zur Lösung

(x - 4)^{\frac{7}{2}} - 16 (x - 4)^{\frac{3}{2}}

Schreibe

(x - 4)^{\frac{7}{2}}

um:

(x - 4)^{7}

= (x - 4)^{7} - 16 (x - 4)^{\frac{3}{2}}

Schreibe

(x - 4)^{\frac{3}{2}}

um:

(x - 4)^{3}

= (x - 4)^{7} - 16 (x - 4)^{3}

Klammere gleiche Terme aus

(x - 4)^{3} : (x - 4)^{3} ((x - 4)^{4} - 16)

= (x - 4)^{3} ((x - 4)^{4} - 16)

Faktorisiere

(x - 4)^{4} - 16 : ((x - 4)^{2} + 4) (x - 4 + 2) (x - 4 - 2)

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

Vereinfache

(x - 4)^{3} ((x - 4)^{2} + 4) (x - 4 + 2) (x - 4 - 2) : x (x - 4)^{3} (x - 4 + 2) (x - 4 - 2)

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

(x - 4)^{3} = (x - 4)^{\frac{3}{2}}

= x (x - 4 + 2) (x - 4 - 2) (x - 4)^{\frac{3}{2}}

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