faktorisieren 4x^2-12x^2

Lösung

faktorisieren

4 x^{2} - 12 x^{2}

- 4 (1 + 3) (3 - 1) x^{2}

Schritte zur Lösung

4 x^{2} - 12 x^{2}

Schreibe

4 x^{2}

um:

(2 x)^{2}

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

Schreibe

(2 x)^{2} - 12 x^{2}

um:

(2 x)^{2} - (12 x)^{2}

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

Wende Formel zur Differenz von zwei Quadraten an:

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

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

= (2 x + 12 x) (2 x - 12 x)

Fasse zusammen

= (23 x + 2 x) (2 x - 23 x)

Faktorisiere

23 x + 2 x : 2 x (3 + 1)

= 2 (1 + 3) x (2 x - 23 x)

Faktorisiere

2 x - 23 x : - 2 x (3 - 1)

= - 2 x (3 + 1) \cdot 2 x (3 - 1)

Fasse zusammen

= - 4 (3 + 1) (3 - 1) x^{2}

Rewrite in standard form

= - 4 (1 + 3) (3 - 1) x^{2}

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f a c t or (4 x^{2} + 2 y) + (3 x + y^{2})

f a c t or 9 (x - 2)^{2} - 24 (x - 2) + 16

f a c t or 10 cos^{2} (x) + cos (x) - 11

f a c t or 2 π + \frac{4}{3} π