faktorisieren 8x^6-27y^6

Lösung

faktorisieren

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

(2 x^{2} - 3 y^{2}) (4 x^{4} + 6 x^{2} y^{2} + 9 y^{4})

Schritte zur Lösung

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

Wende Exponentenregel an

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

Wende Formel zur Differenz von dritten Potenzen an:

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

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

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

Vereinfache

(2 x^{2})^{2} + 2 x^{2} \cdot 3 y^{2} + (3 y^{2})^{2} : 4 x^{4} + 6 x^{2} y^{2} + 9 y^{4}

= (2 x^{2} - 3 y^{2}) (4 x^{4} + 6 x^{2} y^{2} + 9 y^{4})

(2 x + 3) (x + 4) = 0

s im pl i f y - 3

- 3 g + 6 = 9 g^{2}

\frac{y + 1}{4} - \frac{y}{3} > 1 + \frac{2 y - 1}{6}

7 x - 3 = 32