faktorisieren 27x^6+8y^3

Lösung

faktorisieren

27 x^{6} + 8 y^{3}

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

Schritte zur Lösung

27 x^{6} + 8 y^{3}

Wende Exponentenregel an

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

Wende Formel zur Summe von dritten Potenzen an:

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

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

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

Vereinfache

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

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

s im pl i f y \frac{1}{8} + \frac{3}{20}

s im pl i f y - 3 + 4 (a - 3 b + 2) - 5 (2 - a + 3 b)

s im pl i f y \frac{( - 4 + 2 i )}{( 1 + i )}

e x p an d 3 a (2 b - 7)

s im pl i f y - 17 + 2 (6 x - 1) + 5