faktorisieren 64x^6-y^9

Lösung

faktorisieren

64 x^{6} - y^{9}

(4 x^{2} - y^{3}) (16 x^{4} + 4 x^{2} y^{3} + y^{6})

Schritte zur Lösung

64 x^{6} - y^{9}

Wende Exponentenregel an

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

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

Vereinfache

(4 x^{2})^{2} + 4 x^{2} y^{3} + (y^{3})^{2} : 16 x^{4} + 4 x^{2} y^{3} + y^{6}

= (4 x^{2} - y^{3}) (16 x^{4} + 4 x^{2} y^{3} + y^{6})

f a c t or 225 m^{2} - 100 n^{2}

f a c t or x^{2} + x y + 9 x + 9 y

s im pl i f y (a + b + c)^{2} + (a - b - c)^{2}

\frac{( 8 ^{\frac{1}{3}} \times 1 6 ^{\frac{1}{3}} )}{3 2 ^{- 1}} /3

s im pl i f y \frac{( 10 x ^{2} + 19 x + 6 )}{( 2 x + 3 )}