faktorisieren x^4-4x^2y^2+4y^4

Lösung

faktorisieren

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

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

Schritte zur Lösung

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

Zerlege die Ausdrücke in Gruppen

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

Klammere

x^{2}

aus

x^{4} - 2 x^{2} y^{2}

aus

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

Klammere

- 2 y^{2}

aus

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

aus

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

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

Klammere gleiche Terme aus

x^{2} - 2 y^{2}

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

Wende Exponentenregel an:

aa = a^{2}

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

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

f a c t or j^{2} k^{2} + 3 j k^{2}

2 x + 7 - 2 (x - 1) = 3 (x + 3)

s im pl i f y \frac{4 ^{2}}{4 ^{- 1}}

s im pl i f y \frac{- 1}{2} + 1

\frac{x - 3}{2} - \frac{x - 4}{3} < 1