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Beliebt Algebra >

faktorisieren r^6+s^6

Lösung

faktorisieren

r^{6} + s^{6}

Lösung

(r^{2} + s^{2}) (r^{4} - r^{2} s^{2} + s^{4})

Schritte zur Lösung

r^{6} + s^{6}

Wende Exponentenregel an

= (r^{2})^{3} + (s^{2})^{3}

Wende Formel zur Summe von dritten Potenzen an:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(r^{2})^{3} + (s^{2})^{3} = (r^{2} + s^{2}) ((r^{2})^{2} - r^{2} s^{2} + (s^{2})^{2})

= (r^{2} + s^{2}) ((r^{2})^{2} - r^{2} s^{2} + (s^{2})^{2})

Vereinfache

(r^{2})^{2} - r^{2} s^{2} + (s^{2})^{2} : r^{4} - r^{2} s^{2} + s^{4}

= (r^{2} + s^{2}) (r^{4} - r^{2} s^{2} + s^{4})

Beliebte Beispiele

vereinfachen (4x^2y^5)^{-2}

s im pl i f y (4 x^{2} y^{5})^{- 2}

5 x^{2} + 2 x + 1 = 0

\frac{1}{3} (1)^{2}

x^{2} + 20 x = 0

88=([(1.96+x)10]^2)/((25-12)^2)

88 = \frac{[ ( 1.96 + x ) 10 ] ^{2}}{( 25 - 12 ) ^{2}}