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Beliebt Algebra >

faktorisieren 27x^6-125y^6

Lösung

faktorisieren

27 x^{6} - 125 y^{6}

Lösung

(3 x^{2} - 5 y^{2}) (9 x^{4} + 15 x^{2} y^{2} + 25 y^{4})

Schritte zur Lösung

27 x^{6} - 125 y^{6}

Wende Exponentenregel an

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

Wende Formel zur Differenz von dritten Potenzen an:

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

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

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

Vereinfache

(3 x^{2})^{2} + 3 x^{2} \cdot 5 y^{2} + (5 y^{2})^{2} : 9 x^{4} + 15 x^{2} y^{2} + 25 y^{4}

= (3 x^{2} - 5 y^{2}) (9 x^{4} + 15 x^{2} y^{2} + 25 y^{4})

Beliebte Beispiele

2 v^{2} - 47 = 61

6 x + 7 = 5 x + 13

8 (3 n + 5) = - 32

(x - 5)^{2} = - 7

vereinfachen (7/2)^8

s im pl i f y (\frac{7}{2})^{8}