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Beliebt Algebra >

faktorisieren x^6-8x^6

Lösung

faktorisieren

x^{6} - 8 x^{6}

Lösung

- 7 x^{6}

Schritte zur Lösung

x^{6} - 8 x^{6}

Schreibe

8 x^{6}

um:

(2 x^{2})^{3}

= x^{6} - (2 x^{2})^{3}

Wende Exponentenregel an:

a^{b c} = (a^{b})^{c}

x^{6} = (x^{2})^{3}

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

Wende Formel zur Differenz von dritten Potenzen an:

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

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

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

Vereinfache

(x^{2} - 2 x^{2}) (x^{4} + x^{2} \cdot 2 x^{2} + (2 x^{2})^{2}) : - 7 x^{6}

= - 7 x^{6}

Beliebte Beispiele

16 - x^{2} \geq 0

faktorisieren 16x^2+40x+25-y^2

f a c t or 16 x^{2} + 40 x + 25 - y^{2}

4 x - 1 < 6 x - 5

-0.85t-0.85t-3.9=-8.15

- 0.85 t - 0.85 t - 3.9 = - 8.15

- 6 < 3 n + 9 < 21