faktorisieren (x^2+xy^2)^2-(xy+y^2)^2

Lösung

faktorisieren

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

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

Schritte zur Lösung

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

Wende Formel zur Differenz von zwei Quadraten an:

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

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

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

Vereinfache

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

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

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

s im pl i f y 32.5 \cdot \frac{1}{71.1} \cdot \frac{4}{4} \cdot 56.11

5^{x^{2}} > 2^{x}

- \frac{2}{3} ln (1 - 9^{\frac{3}{2}}) = 0 + C

f a c t or 4 - x^{2}