faktorisieren (12x+7)^2-4(2x-1)^2

Lösung

faktorisieren

(12 x + 7)^{2} - 4 (2 x - 1)^{2}

(16 x + 5) (8 x + 9)

Schritte zur Lösung

(12 x + 7)^{2} - 4 (2 x - 1)^{2}

Vereinfache

4 (2 x - 1)^{2} : (2 (2 x - 1))^{2}

= (12 x + 7)^{2} - (2 (2 x - 1))^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(12 x + 7)^{2} - (2 (2 x - 1))^{2} = ((12 x + 7) + 2 (2 x - 1)) ((12 x + 7) - 2 (2 x - 1))

= ((12 x + 7) + 2 (2 x - 1)) ((12 x + 7) - 2 (2 x - 1))

Vereinfache

((12 x + 7) + 2 (2 x - 1)) ((12 x + 7) - 2 (2 x - 1)) : (16 x + 5) (8 x + 9)

= (16 x + 5) (8 x + 9)

s im pl i f y \frac{1}{1 - ( \frac{1}{2} ) ^{2}}

8 - 4 ∣ 1 - x ∣ = - 24

f a c t or 3 x^{2} + 27 x - 30

s im pl i f y \frac{1}{1 + \frac{1}{1 + \frac{1}{2}}}

f a c t or 2 x^{2} y - 2 x y^{2} + 4 x y