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

Lösung

faktorisieren

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

- 3 (8 x + 5) (2 x + 1)

Schritte zur Lösung

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

Wende Formel zur Differenz von zwei Quadraten an:

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

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

= ((x + 1) + (7 x + 4)) ((x + 1) - (7 x + 4))

Vereinfache

((x + 1) + (7 x + 4)) ((x + 1) - (7 x + 4)) : (8 x + 5) (- 6 x - 3)

= (8 x + 5) (- 6 x - 3)

Faktorisiere

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

= (8 x + 5) (- 3 (2 x + 1))

Apply rule:

a (- b) = - ab

(8 x + 5) (- 3 (2 x + 1)) = - (8 x + 5) \cdot 3 (2 x + 1)

= - (8 x + 5) \cdot 3 (2 x + 1)

= - 3 (8 x + 5) (2 x + 1)

s im pl i f y - 4 \cdot 7

f a c t or 7 x^{2} + 5 x^{4}

x (5 x - 7) = 1

s im pl i f y \frac{1}{7} \cdot \frac{1}{2}

3 x^{2} + 7 x - 1 = 0