faktorisieren x^8+x^4y^4+y^8

Lösung

faktorisieren

x^{8} + x^{4} y^{4} + y^{8}

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

Schritte zur Lösung

x^{8} + x^{4} y^{4} + y^{8}

Addiere und subtrahiere

x^{4} y^{4}

= x^{8} + 2 x^{4} y^{4} + y^{8} - x^{4} y^{4}

Faktorisiere

x^{8} + 2 x^{4} y^{4} + y^{8} : (x^{4} + y^{4})^{2}

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

Wende Exponentenregel an

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

Faktorisiere

(x^{4} + y^{4})^{2} - (x^{2} y^{2})^{2} : (x^{4} + y^{4} + x^{2} y^{2}) (x^{4} + y^{4} - x^{2} y^{2})

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

s im pl i f y (- 6.7 + 2 z) (- 1.5)

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

e x p an d (- y^{2} - 1)^{3}

f a c t or 2 x^{3} - 6 x^{2} + 6 x - 2

e x p an d (1 - h)^{3}