faktorisieren 64x^6-125y^6

Lösung

faktorisieren

64 x^{6} - 125 y^{6}

(4 x^{2} - 5 y^{2}) (16 x^{4} + 20 x^{2} y^{2} + 25 y^{4})

Schritte zur Lösung

64 x^{6} - 125 y^{6}

Wende Exponentenregel an

= (4 x^{2})^{3} - (5 y^{2})^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(4 x^{2})^{3} - (5 y^{2})^{3} = (4 x^{2} - 5 y^{2}) ((4 x^{2})^{2} + 4 x^{2} \cdot 5 y^{2} + (5 y^{2})^{2})

= (4 x^{2} - 5 y^{2}) ((4 x^{2})^{2} + 4 x^{2} \cdot 5 y^{2} + (5 y^{2})^{2})

Vereinfache

(4 x^{2})^{2} + 4 x^{2} \cdot 5 y^{2} + (5 y^{2})^{2} : 16 x^{4} + 20 x^{2} y^{2} + 25 y^{4}

= (4 x^{2} - 5 y^{2}) (16 x^{4} + 20 x^{2} y^{2} + 25 y^{4})

s im pl i f y (- 9 + i) (- 9 - i)

3 (x - 1) + 5 = 6 - (x + 2)

s im pl i f y (- \frac{1}{2 6 - x})^{2}

s im pl i f y \frac{4}{21}

x = lo g_{5} (\frac{1}{3125})