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Beliebt Algebra >

faktorisieren 16u^8-8u^4+1

Lösung

faktorisieren

16 u^{8} - 8 u^{4} + 1

Lösung

(2 u^{2} + 1)^{2} (2 u + 1)^{2} (2 u - 1)^{2}

Schritte zur Lösung

16 u^{8} - 8 u^{4} + 1

Angenommen

v = u^{2}

= 16 v^{4} - 8 v^{2} + 1

Faktorisiere

16 v^{4} - 8 v^{2} + 1 : (2 v + 1) (2 v - 1) (2 v + 1) (2 v - 1)

= (2 v + 1) (2 v - 1) (2 v + 1) (2 v - 1)

Setze in

v = u^{2}

ein

= (2 u^{2} + 1) (2 u^{2} - 1) (2 u^{2} + 1) (2 u^{2} - 1)

Fasse zusammen

= (2 u^{2} + 1)^{2} (2 u^{2} - 1)^{2}

Wende Exponentenregel an:

a^{m} b^{m} = (ab)^{m},

angenommen

a \geq 0, b \geq 0

(2 u^{2} + 1)^{2} (2 u^{2} - 1)^{2} = ((2 u^{2} + 1) (2 u^{2} - 1))^{2}

= ((2 u^{2} + 1) (2 u^{2} - 1))^{2}

Faktorisiere

(2 u^{2} + 1) (2 u^{2} - 1) : (2 u^{2} + 1) (2 u + 1) (2 u - 1)

= ((2 u^{2} + 1) (2 u + 1) (2 u - 1))^{2}

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} b^{n}

= (2 u^{2} + 1)^{2} (2 u + 1)^{2} (2 u - 1)^{2}

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