faktorisieren 16x^4+9y^4+24x^2*y^2

Lösung

faktorisieren

16 x^{4} + 9 y^{4} + 24 x^{2} \cdot y^{2}

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

Schritte zur Lösung

16 x^{4} + 9 y^{4} + 24 x^{2} y^{2}

Group by common factors

= 16 x^{4} + 24 x^{2} y^{2} + 9 y^{4}

Zerlege die Ausdrücke in Gruppen

= (16 x^{4} + 12 x^{2} y^{2}) + (12 x^{2} y^{2} + 9 y^{4})

Klammere

4 x^{2}

aus

16 x^{4} + 12 x^{2} y^{2}

aus

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

Klammere

3 y^{2}

aus

12 x^{2} y^{2} + 9 y^{4}

aus

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

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

Klammere gleiche Terme aus

4 x^{2} + 3 y^{2}

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

Wende Exponentenregel an:

aa = a^{2}

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

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

e x p an d (2 a + 3) (3 a + 2 b)

s im pl i f y x 3 y^{23}

s im pl i f y (15 x^{2} - 2 x + 10) + (13 x + 15)

s im pl i f y 31 c 9 x - 5 a

e x p an d a (2 a + b)