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Beliebt Algebra >

faktorisieren 5832m^{15}n^{24}+p^{21}

Lösung

faktorisieren

5832 m^{15} n^{24} + p^{21}

Lösung

(18 m^{5} n^{8} + p^{7}) (324 m^{10} n^{16} - 18 m^{5} n^{8} p^{7} + p^{14})

Schritte zur Lösung

5832 m^{15} n^{24} + p^{21}

Schreibe

5832 m^{15} n^{24}

um:

(18 m^{5} n^{8})^{3}

= (18 m^{5} n^{8})^{3} + p^{21}

Wende Exponentenregel an:

a^{b c} = (a^{b})^{c}

p^{21} = (p^{7})^{3}

= (18 m^{5} n^{8})^{3} + (p^{7})^{3}

Wende Formel zur Summe von dritten Potenzen an:

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

(18 m^{5} n^{8})^{3} + (p^{7})^{3} = (18 m^{5} n^{8} + p^{7}) ((18 m^{5} n^{8})^{2} - p^{7} 18 m^{5} n^{8} + p^{14})

= (p^{7} + 18 m^{5} n^{8}) (p^{14} - p^{7} 18 m^{5} n^{8} + (18 m^{5} n^{8})^{2})

Vereinfache

(18 m^{5} n^{8} + p^{7}) ((18 m^{5} n^{8})^{2} - p^{7} \cdot 18 m^{5} n^{8} + p^{14}) : (18 m^{5} n^{8} + p^{7}) (324 m^{10} n^{16} - 18 m^{5} n^{8} p^{7} + p^{14})

= (18 m^{5} n^{8} + p^{7}) (324 m^{10} n^{16} - 18 m^{5} n^{8} p^{7} + p^{14})

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