faktorisieren x^9-y^9

Lösung

faktorisieren

x^{9} - y^{9}

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

Schritte zur Lösung

x^{9} - y^{9}

Wende Exponentenregel an

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

Wende Formel zur Differenz von dritten Potenzen an:

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

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

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

Vereinfache

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

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

Faktorisiere

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

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

s im pl i f y \frac{7 ( ( 16 ( 2 ) ^{3} ) - 2 )}{5 ^{\frac{4}{5}}}

f a c t or 100 x^{2} - 9 y^{2}

(x - 8)^{2} = - 2

f a c t or 100 b^{2} - 90 b + 20

0 \geq x \geq 10