faktorisieren 64x^3-125y^6

Lösung

faktorisieren

64 x^{3} - 125 y^{6}

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

Schritte zur Lösung

64 x^{3} - 125 y^{6}

Wende Exponentenregel an

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

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

Vereinfache

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

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

s im pl i f y \frac{8}{9} - \frac{2}{3}

9 x - 15 = 75

0.2 p + 2.4 = 1.6 p - 1.2 + 0.6 p

5 - 3 z \geq - 7

f a c t or x^{4} y^{3} + 7 x^{2} y - 3 x^{3} y^{3}