faktorisieren (x^2-3)^2-(x-9)^2

Lösung

faktorisieren

(x^{2} - 3)^{2} - (x - 9)^{2}

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

Schritte zur Lösung

(x^{2} - 3)^{2} - (x - 9)^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(x^{2} - 3)^{2} - (x - 9)^{2} = ((x^{2} - 3) + (x - 9)) ((x^{2} - 3) - (x - 9))

= ((x^{2} - 3) + (x - 9)) ((x^{2} - 3) - (x - 9))

Vereinfache

((x^{2} - 3) + (x - 9)) ((x^{2} - 3) - (x - 9)) : (x^{2} - 12 + x) (x^{2} - x + 6)

= (x^{2} - 12 + x) (x^{2} - x + 6)

= (x^{2} + x - 12) (x^{2} - x + 6)

Faktorisiere

x^{2} + x - 12 : (x - 3) (x + 4)

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

f a c t or 16 b^{2} - 81

s im pl i f y \frac{1}{5 27}

s im pl i f y (- 4 x^{2} + 6 x + 1) + (5 x + 7)

s im pl i f y (- z)^{3} (3 z^{4})

s im pl i f y - 3 (7 f + 3 f + 9) - 4 f