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Beliebt Algebra >

faktorisieren (x+y)^3+512(m-n)^3

Lösung

faktorisieren

(x + y)^{3} + 512 (m - n)^{3}

Lösung

(x + y + 8 (m - n)) ((x + y)^{2} - 8 (x + y) (m - n) + 64 (m - n)^{2})

Schritte zur Lösung

(x + y)^{3} + 512 (m - n)^{3}

Schreibe

(x + y)^{3} + 512 (m - n)^{3}

um:

(x + y)^{3} + (8 (m - n))^{3}

= (x + y)^{3} + (8 (m - n))^{3}

Wende Formel zur Summe von dritten Potenzen an:

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

(x + y)^{3} + (8 (m - n))^{3} = ((x + y) + 8 (m - n)) ((x + y)^{2} - 8 (x + y) (m - n) + 8^{2} (m - n)^{2})

= ((x + y) + 8 (m - n)) ((x + y)^{2} - 8 (x + y) (m - n) + 8^{2} (m - n)^{2})

Fasse zusammen

= (x + y + 8 (m - n)) (64 (m - n)^{2} - 8 (x + y) (m - n) + (x + y)^{2})

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