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Beliebt Algebra >

faktorisieren 27u^3+8v^3

Lösung

faktorisieren

27 u^{3} + 8 v^{3}

Lösung

(3 u + 2 v) (9 u^{2} - 6 uv + 4 v^{2})

Schritte zur Lösung

27 u^{3} + 8 v^{3}

Wende Exponentenregel an

= (3 u)^{3} + (2 v)^{3}

Wende Formel zur Summe von dritten Potenzen an:

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

(3 u)^{3} + (2 v)^{3} = (3 u + 2 v) ((3 u)^{2} - 3 u \cdot 2 v + (2 v)^{2})

= (3 u + 2 v) ((3 u)^{2} - 3 u \cdot 2 v + (2 v)^{2})

Vereinfache

(3 u)^{2} - 3 u \cdot 2 v + (2 v)^{2} : 9 u^{2} - 6 uv + 4 v^{2}

= (3 u + 2 v) (9 u^{2} - 6 uv + 4 v^{2})

Beliebte Beispiele

x - 3 > 7

- \frac{2}{3} b = 75

2 u^{2} + 7 u + 5 = 0

m^{2} - 24 = - 2 m

5(x-3)+8x=6x-5+x

5 (x - 3) + 8 x = 6 x - 5 + x