faktorisieren 8x^5y^3+32x^2y^8-64x^4y^2

Lösung

faktorisieren

8 x^{5} y^{3} + 32 x^{2} y^{8} - 64 x^{4} y^{2}

8 x^{2} y^{2} (x^{3} y + 4 y^{6} - 8 x^{2})

Schritte zur Lösung

8 x^{5} y^{3} + 32 x^{2} y^{8} - 64 x^{4} y^{2}

Wende Exponentenregel an:

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

x^{5} y^{3} = x^{2} x^{3} y^{2} y, x^{2} y^{8} = x^{2} y^{2} y^{6}, x^{4} y^{2} = x^{2} x^{2} y^{2}

= 8 x^{2} x^{3} y^{2} y + 32 x^{2} y^{2} y^{6} - 64 x^{2} x^{2} y^{2}

Schreibe

- 64

um:

8 \cdot 8

Schreibe

32

um:

4 \cdot 8

= 8 x^{2} x^{3} y^{2} y + 4 \cdot 8 x^{2} y^{2} y^{6} + 8 \cdot 8 x^{2} x^{2} y^{2}

Klammere gleiche Terme aus

8 x^{2} y^{2}

= 8 x^{2} y^{2} (x^{3} y + 4 y^{6} - 8 x^{2})

x (x + 2) = 5 (x + x + 2) - 1

s im pl i f y π \cdot 3^{2}

∣ x - 4 ∣ < 7

s im pl i f y 8 \cdot (11 i + 2)

(x - 0.4)^{2} = - 255.84