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Beliebt Algebra >

faktorisieren a^5-a^3b^2-a^2b^3+b^5

Lösung

faktorisieren

a^{5} - a^{3} b^{2} - a^{2} b^{3} + b^{5}

Lösung

(a + b) (a - b)^{2} (a^{2} + ab + b^{2})

Schritte zur Lösung

a^{5} - a^{3} b^{2} - a^{2} b^{3} + b^{5}

= (a^{5} - a^{3} b^{2}) + (b^{5} - a^{2} b^{3})

Klammere

a^{3}

aus

a^{5} - a^{3} b^{2}

aus

: a^{3} (a^{2} - b^{2})

Klammere

b^{3}

aus

b^{5} - a^{2} b^{3}

aus

: b^{3} (b^{2} - a^{2})

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

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

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

Klammere gleiche Terme aus

a^{2} - b^{2}

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

Faktorisiere

a^{2} - b^{2} : (a + b) (a - b)

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

Faktorisiere

a^{3} - b^{3} : (a - b) (a^{2} + ab + b^{2})

= (a + b) (a - b) (a - b) (a^{2} + ab + b^{2})

Wende Exponentenregel an:

aa = a^{2}

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

= (a + b) (a - b)^{2} (a^{2} + ab + b^{2})

Beliebte Beispiele

faktorisieren-x^2+8x-7

f a c t or - x^{2} + 8 x - 7

x^{2} + 3 x < 4

- x - 3 = 2 x - 6

vereinfachen ((3m^2n^7)/m)^5

s im pl i f y (\frac{3 m ^{2} n ^{7}}{m})^{5}

faktorisieren 8x^2-x-9

f a c t or 8 x^{2} - x - 9