faktorisieren 36x^2-27x^2

Lösung

faktorisieren

36 x^{2} - 27 x^{2}

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

Schritte zur Lösung

36 x^{2} - 27 x^{2}

Schreibe

36 x^{2}

um:

(6 x)^{2}

= (6 x)^{2} - 27 x^{2}

Schreibe

(6 x)^{2} - 27 x^{2}

um:

(6 x)^{2} - (27 x)^{2}

= (6 x)^{2} - (27 x)^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(6 x)^{2} - (27 x)^{2} = (6 x + 27 x) (6 x - 27 x)

= (6 x + 27 x) (6 x - 27 x)

Fasse zusammen

= (33 x + 6 x) (6 x - 33 x)

Faktorisiere

33 x + 6 x : 3 x (3 + 2)

= 3 (2 + 3) x (6 x - 33 x)

Faktorisiere

6 x - 33 x : - 3 x (3 - 2)

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

Fasse zusammen

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

Rewrite in standard form

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

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