faktorisieren 40x^9y^8+24x^2y^5+16x^7y^2

Lösung

faktorisieren

40 x^{9} y^{8} + 24 x^{2} y^{5} + 16 x^{7} y^{2}

8 x^{2} y^{2} (5 x^{7} y^{6} + 3 y^{3} + 2 x^{5})

Schritte zur Lösung

40 x^{9} y^{8} + 24 x^{2} y^{5} + 16 x^{7} y^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} a^{c}

x^{9} y^{8} = x^{2} x^{7} y^{2} y^{6}, x^{2} y^{5} = x^{2} y^{2} y^{3}, x^{7} y^{2} = x^{2} x^{5} y^{2}

= 40 x^{2} x^{2} x^{5} y^{2} y^{6} + 24 x^{2} y^{2} y^{3} + 16 x^{2} x^{5} y^{2}

Schreibe

16

um:

2 \cdot 8

Schreibe

24

um:

3 \cdot 8

= 5 \cdot 8 x^{2} x^{2} x^{5} y^{2} y^{6} + 3 \cdot 8 x^{2} y^{2} y^{3} + 2 \cdot 8 x^{2} x^{5} y^{2}

Klammere gleiche Terme aus

8 x^{2} y^{2}

= 8 x^{2} y^{2} (5 x^{7} y^{6} + 3 y^{3} + 2 x^{5})

x^{2} - 2 x + 6 \leq 0

- x = - 3 x^{2} + 1

x^{2} + (12 - x)^{2} = 74

(x + 1)^{2} < 0

f a c t or 4 (x + 2)^{2} - 5 (x + 2) + 1