faktorisieren (3x-7)^2-(4x+3)^2

Lösung

faktorisieren

(3 x - 7)^{2} - (4 x + 3)^{2}

- (7 x - 4) (x + 10)

Schritte zur Lösung

(3 x - 7)^{2} - (4 x + 3)^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(3 x - 7)^{2} - (4 x + 3)^{2} = ((3 x - 7) + (4 x + 3)) ((3 x - 7) - (4 x + 3))

= ((3 x - 7) + (4 x + 3)) ((3 x - 7) - (4 x + 3))

Vereinfache

((3 x - 7) + (4 x + 3)) ((3 x - 7) - (4 x + 3)) : (7 x - 4) (- x - 10)

= (7 x - 4) (- x - 10)

Faktorisiere

- x - 10 : - (x + 10)

= (7 x - 4) (- (x + 10))

Apply rule:

a (- b) = - ab

(7 x - 4) (- (x + 10)) = - (7 x - 4) (x + 10)

= - (7 x - 4) (x + 10)

7 v - 5 > 65 or - 3 v - 2 \geq - 2

5 x^{2} - 34 x = - 24

2 x + 8 = 3 + 2 x

s im pl i f y (16 y^{8})^{\frac{3}{4}}

\frac{x + 14}{x + 2} \geq 3