faktorisieren a^2b^6-1

Lösung

faktorisieren

a^{2} b^{6} - 1

(a b^{3} + 1) (a b^{3} - 1)

Schritte zur Lösung

a^{2} b^{6} - 1

a^{2} b^{6} = (a b^{3})^{2}

1 = 1^{2}

= (a b^{3})^{2} - 1^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(a b^{3})^{2} - 1^{2} = (a b^{3} + 1) (a b^{3} - 1)

= (a b^{3} + 1) (a b^{3} - 1)

s im pl i f y \frac{5}{61}

s im pl i f y (3 x + 2) (x + y - z) - (3 x + 2) - (x + y - 1) (3 x + 2)

f a c t or 27 u^{4} v^{5} - 63 u^{3} v^{6}

s im pl i f y \frac{x ^{3} - 3 x ^{2}}{x + 8} \cdot \frac{x ^{2} - 64}{x ^{2} - 11 x + 24}

f a c t or 4 x^{5} - 2 x^{4} + 30 x^{3} - 15 x^{2} + 50 x - 25