faktorisieren (x^2+9)^2-36x^2

Lösung

faktorisieren

(x^{2} + 9)^{2} - 36 x^{2}

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

Schritte zur Lösung

(x^{2} + 9)^{2} - 36 x^{2}

Vereinfache

36 x^{2} : (6 x)^{2}

= (x^{2} + 9)^{2} - (6 x)^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(x^{2} + 9)^{2} - (6 x)^{2} = ((x^{2} + 9) + 6 x) ((x^{2} + 9) - 6 x)

= ((x^{2} + 9) + 6 x) ((x^{2} + 9) - 6 x)

Apply rule:

(a) = a

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

= (x^{2} + 9 + 6 x) (x^{2} + 9 - 6 x)

= (x^{2} + 6 x + 9) (x^{2} - 6 x + 9)

Faktorisiere

x^{2} + 6 x + 9 : (x + 3)^{2}

Faktorisiere

x^{2} - 6 x + 9 : (x - 3)^{2}

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

f a c t or 2^{n + 1} - 2^{n}

\frac{x ( x + 2 )}{( x - 5 )} - 2 < x < 0

∣ x - 2 ∣ = ∣ 3 x + 3 ∣

\frac{1}{x + 2} \leq \frac{3}{x - 5}

5 x^{2} - 19 x - 4 = 0