faktorisieren sin^4(x)-1

Lösung

faktorisieren

sin^{4} (x) - 1

(sin^{2} (x) + 1) (sin (x) + 1) (sin (x) - 1)

Schritte zur Lösung

sin^{4} (x) - 1

sin^{4} (x) = (sin^{2} (x))^{2}

1 = 1^{2}

= (sin^{2} (x))^{2} - 1^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(sin^{2} (x))^{2} - 1^{2} = (sin^{2} (x) + 1) (sin^{2} (x) - 1)

= (sin^{2} (x) + 1) (sin^{2} (x) - 1)

Faktorisiere

sin^{2} (x) - 1 : (sin (x) + 1) (sin (x) - 1)

= (sin^{2} (x) + 1) (sin (x) + 1) (sin (x) - 1)

s im pl i f y 25 x^{2} - 100 x \cdot y^{2} + 100 y^{4}

s im pl i f y \frac{\frac{1}{10} v}{v}

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

s im pl i f y \frac{( 4 b ^{2} \cdot 2 b ^{3} )}{( 8 b )}

s im pl i f y \frac{( x ^{3} + 2 x ^{2} + 3 x )}{2 \cdot x}