faktorisieren 1-4x^2+12xy-9y^2

Lösung

faktorisieren

1 - 4 x^{2} + 12 x y - 9 y^{2}

(1 + 2 x - 3 y) (1 - 2 x + 3 y)

Schritte zur Lösung

1 - 4 x^{2} + 12 x y - 9 y^{2}

Faktorisiere

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

= 1 - (2 x - 3 y)^{2}

Schreibe

1

um:

1^{2}

= 1^{2} - (2 x - 3 y)^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

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

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

Vereinfache

(1 + (2 x - 3 y)) (1 - (2 x - 3 y)) : (1 + 2 x - 3 y) (1 - 2 x + 3 y)

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

e x p an d (5 p^{2} - 4 q)^{3}

s im pl i f y (- 4 x^{3})^{2}

s im pl i f y \frac{5}{8} - \frac{9}{32}

s im pl i f y \frac{( \frac{1}{x} - 1 )}{x - 1}

e x p an d (3 x + 6 y) (x^{2} + 4 x y - 5 y^{2})