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Beliebt Algebra >

faktorisieren m^9n^{15}+p^{21}

Lösung

faktorisieren

m^{9} n^{15} + p^{21}

Lösung

(m^{3} n^{5} + p^{7}) (m^{6} n^{10} - m^{3} n^{5} p^{7} + p^{14})

Schritte zur Lösung

m^{9} n^{15} + p^{21}

Schreibe

m^{9} n^{15}

um:

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

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

Wende Exponentenregel an:

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

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

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

Wende Formel zur Summe von dritten Potenzen an:

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

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

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

Vereinfache

(m^{3} n^{5} + p^{7}) ((m^{3} n^{5})^{2} - p^{7} m^{3} n^{5} + p^{14}) : (m^{3} n^{5} + p^{7}) (m^{6} n^{10} - m^{3} n^{5} p^{7} + p^{14})

= (m^{3} n^{5} + p^{7}) (m^{6} n^{10} - m^{3} n^{5} p^{7} + p^{14})

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