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Beliebt Algebra >

faktorisieren 8c^3-27d^3

Lösung

faktorisieren

8 c^{3} - 27 d^{3}

Lösung

(2 c - 3 d) (4 c^{2} + 6 c d + 9 d^{2})

Schritte zur Lösung

8 c^{3} - 27 d^{3}

Wende Exponentenregel an

= (2 c)^{3} - (3 d)^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(2 c)^{3} - (3 d)^{3} = (2 c - 3 d) ((2 c)^{2} + 2 c \cdot 3 d + (3 d)^{2})

= (2 c - 3 d) ((2 c)^{2} + 2 c \cdot 3 d + (3 d)^{2})

Vereinfache

(2 c)^{2} + 2 c \cdot 3 d + (3 d)^{2} : 4 c^{2} + 6 c d + 9 d^{2}

= (2 c - 3 d) (4 c^{2} + 6 c d + 9 d^{2})

Beliebte Beispiele

vereinfachen (1/a+1/b+1/c)/(1/(ab)+1/(bc)+1/(ac))

s im pl i f y \frac{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}}{\frac{1}{ab} + \frac{1}{b c} + \frac{1}{a c}}

4 y^{2} - 5 y - 3 = 0

n^{2} - 6 n - 19 = 0

1/3 (9x+3)=3x+1

\frac{1}{3} (9 x + 3) = 3 x + 1

∣ 2 k - 1 ∣ < 5