faktorisieren 64x^6-729y^6

Lösung

faktorisieren

64 x^{6} - 729 y^{6}

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

Schritte zur Lösung

64 x^{6} - 729 y^{6}

64 x^{6} = (8 x^{3})^{2}

729 y^{6} = (27 y^{3})^{2}

= (8 x^{3})^{2} - (27 y^{3})^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(8 x^{3})^{2} - (27 y^{3})^{2} = (8 x^{3} + 27 y^{3}) (8 x^{3} - 27 y^{3})

= (8 x^{3} + 27 y^{3}) (8 x^{3} - 27 y^{3})

Faktorisiere

8 x^{3} + 27 y^{3} : (2 x + 3 y) (4 x^{2} - 6 x y + 9 y^{2})

= (2 x + 3 y) (4 x^{2} - 6 x y + 9 y^{2}) (8 x^{3} - 27 y^{3})

Faktorisiere

8 x^{3} - 27 y^{3} : (2 x - 3 y) (4 x^{2} + 6 x y + 9 y^{2})

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

s im pl i f y \frac{5 - ( 3 x )}{4 - 8}

e x p an d a (a + 1) x^{2} + x - a (a - 1)

f a c t or x^{4} + x^{2} + x

s im pl i f y \frac{( 14 x ^{2} - 53 x + 45 )}{( 7 x - 9 )}

s im pl i f y s x (3 s)^{3}