faktorisieren 27x^6-8y^6

Lösung

faktorisieren

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

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

Schritte zur Lösung

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

Wende Exponentenregel an

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

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

Vereinfache

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

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

f a c t or 24 x^{2} - 2 x - 12

1.3 x - 2 - (3.3 x + 5) = 2 x + 1

7 (- 2) - 3 (7) = 11

3 (1)^{4}

s im pl i f y - 7 \cdot \frac{1}{2}