faktorisieren 8x^6-27y^9

Lösung

faktorisieren

8 x^{6} - 27 y^{9}

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

Schritte zur Lösung

8 x^{6} - 27 y^{9}

Wende Exponentenregel an

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

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

Vereinfache

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

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

\frac{2 x + 1}{x + 1} \leq 2

x^{2} - 6 x + 2 = 0

y^{2} = 2 + y

s im pl i f y 8192 - 27

2 x + 5 + 2 x + 3 x = 2 x + 9