faktorisieren 49x^4-4(x^2-3x)^2

Lösung

faktorisieren

49 x^{4} - 4 (x^{2} - 3 x)^{2}

3 x^{2} (3 x - 2) (5 x + 6)

Schritte zur Lösung

49 x^{4} - 4 (x^{2} - 3 x)^{2}

49 x^{4} = (7 x^{2})^{2}

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

= (7 x^{2})^{2} - (2 (x^{2} - 3 x))^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(7 x^{2})^{2} - (2 (x^{2} - 3 x))^{2} = (7 x^{2} + 2 (x^{2} - 3 x)) (7 x^{2} - 2 (x^{2} - 3 x))

= (7 x^{2} + 2 (x^{2} - 3 x)) (7 x^{2} - 2 (x^{2} - 3 x))

Faktorisiere

7 x^{2} + 2 (x^{2} - 3 x) : 3 x (3 x - 2)

Faktorisiere

7 x^{2} - 2 (x^{2} - 3 x) : x (5 x + 6)

= 3 x (3 x - 2) x (5 x + 6)

Wende Exponentenregel an:

aa = a^{2}

xx = x^{2}

= 3 x^{2} (3 x - 2) (5 x + 6)

s im pl i f y \frac{12 x}{6 x y}

- 2 < 2 - 2 x \leq 12

s^{2} - 4 s = 0

s^{2} + 3 s + 2 > 0

f a c t or 3 x^{5} + 18 x^{4} + 27 x^{3} - 12 x^{2} - 36 x