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Beliebt Algebra >

faktorisieren (x-5)^{7/2}-25(x-5)^{3/2}

Lösung

faktorisieren

(x - 5)^{\frac{7}{2}} - 25 (x - 5)^{\frac{3}{2}}

Lösung

x (x - 10) (x - 5)^{\frac{3}{2}}

Schritte zur Lösung

(x - 5)^{\frac{7}{2}} - 25 (x - 5)^{\frac{3}{2}}

Schreibe

(x - 5)^{\frac{7}{2}}

um:

(x - 5)^{7}

= (x - 5)^{7} - 25 (x - 5)^{\frac{3}{2}}

Schreibe

(x - 5)^{\frac{3}{2}}

um:

(x - 5)^{3}

= (x - 5)^{7} - 25 (x - 5)^{3}

Klammere gleiche Terme aus

(x - 5)^{3} : (x - 5)^{3} ((x - 5)^{4} - 25)

= (x - 5)^{3} ((x - 5)^{4} - 25)

Faktorisiere

(x - 5)^{4} - 25 : ((x - 5)^{2} + 5) ((x - 5)^{2} - 5)

= (x - 5)^{3} ((x - 5)^{2} + 5) ((x - 5)^{2} - 5)

Vereinfache

(x - 5)^{3} ((x - 5)^{2} + 5) ((x - 5)^{2} - 5) : x (x - 5)^{3} (x - 10)

= x (x - 5)^{3} (x - 10)

(x - 5)^{3} = (x - 5)^{\frac{3}{2}}

= x (x - 10) (x - 5)^{\frac{3}{2}}

Beliebte Beispiele

x^2+(-1/4)^2=1^2

x^{2} + (- \frac{1}{4})^{2} = 1^{2}

5 x - (x + 1) = 5 - 2 x

(3+x)/(3-x)>= 1

\frac{3 + x}{3 - x} \geq 1

∣ m ∣ + 2 = 11

x^{2} \geq 0