faktorisieren (x^6+x^5+x^4+x^3+x^2+1)^2-x^6

Lösung

faktorisieren

(x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1)^{2} - x^{6}

(x^{6} + x^{5} + x^{4} + 2 x^{3} + x^{2} + 1) (x^{6} + x^{5} + x^{4} + x^{2} + 1)

Schritte zur Lösung

(x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1)^{2} - x^{6}

Vereinfache

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

= (x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1)^{2} - (x^{3})^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1)^{2} - (x^{3})^{2} = ((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) + x^{3}) ((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) - x^{3})

= ((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) + x^{3}) ((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) - x^{3})

Vereinfache

((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) + x^{3}) ((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) - x^{3}) : (x^{6} + x^{5} + x^{4} + 2 x^{3} + x^{2} + 1) (x^{6} + x^{5} + x^{4} + x^{2} + 1)

= (x^{6} + x^{5} + x^{4} + 2 x^{3} + x^{2} + 1) (x^{6} + x^{5} + x^{4} + x^{2} + 1)

s im pl i f y \frac{2 ^{3}}{2 ^{- 2}}

y - 3 = - 3 y - 43

f a c t or 9 m^{2} + 36 m + 36

∣ x - 4 ∣ \leq 2 - x

\frac{p}{5} = - 32