faktorisieren w^2+w^{12}+w^{32}+w^{42}

Lösung

faktorisieren

w^{2} + w^{12} + w^{32} + w^{42}

w^{2} (w^{2} + 1)^{2} (w^{8} - w^{6} + w^{4} - w^{2} + 1)^{2} (w^{20} - w^{10} + 1)

Schritte zur Lösung

w^{2} + w^{12} + w^{32} + w^{42}

Schreibe in der Standard Form

= w^{42} + w^{32} + w^{12} + w^{2}

Klammere gleiche Terme aus

w^{2} : w^{2} (w^{40} + w^{30} + w^{10} + 1)

= w^{2} (w^{40} + w^{30} + w^{10} + 1)

Faktorisiere

w^{40} + w^{30} + w^{10} + 1 : (w^{2} + 1) (w^{8} - w^{6} + w^{4} - w^{2} + 1) (w^{2} + 1) (w^{8} - w^{6} + w^{4} - w^{2} + 1) (w^{20} - w^{10} + 1)

= w^{2} (w^{2} + 1) (w^{8} - w^{6} + w^{4} - w^{2} + 1) (w^{2} + 1) (w^{8} - w^{6} + w^{4} - w^{2} + 1) (w^{20} - w^{10} + 1)

Vereinfache

= w^{2} (w^{2} + 1)^{2} (w^{8} - w^{6} + w^{4} - w^{2} + 1)^{2} (w^{20} - w^{10} + 1)

s im pl i f y 5 a (x - y) + 3 b (y - x) - (x - y)

s im pl i f y 9^{x} - 9 (3^{x + 2}) + 243

f a c t or x^{3} y - 6 x^{2} y^{3} + 9 x^{2} y^{2}

s im pl i f y l^{- 1} (\frac{1}{( s + 3 ) ^{n}})

e x p an d x^{2} - (k + 2) x + k + 5