faktorisieren 0.027j^3-0.216k^6

Lösung

faktorisieren

0.027 j^{3} - 0.216 k^{6}

(0.3 j - 0.6 k^{2}) (0.09 j^{2} + 0.18 j k^{2} + 0.36 k^{4})

Schritte zur Lösung

0.027 j^{3} - 0.216 k^{6}

Schreibe

0.027 j^{3} - 0.216 k^{6}

um:

(3 0.027 j)^{3} - (3 0.216 k^{2})^{3}

= (3 0.027 j)^{3} - (3 0.216 k^{2})^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(3 0.027 j)^{3} - (3 0.216 k^{2})^{3} = (3 0.027 j - 3 0.216 k^{2}) ((3 0.027)^{2} j^{2} + 3 0.027 3 0.216 j k^{2} + (3 0.216)^{2} k^{4})

= (3 0.027 j - 3 0.216 k^{2}) ((3 0.027)^{2} j^{2} + 3 0.027 3 0.216 j k^{2} + (3 0.216)^{2} k^{4})

Fasse zusammen

= (3 0.027 j - 3 0.216 k^{2}) (0.02 7^{\frac{2}{3}} j^{2} + 3 0.005832 j k^{2} + 0.21 6^{\frac{2}{3}} k^{4})

3 0.027 = 0.3

= (0.3 j - 3 0.216 k^{2}) (0.02 7^{\frac{2}{3}} j^{2} + 3 0.005832 j k^{2} + 0.21 6^{\frac{2}{3}} k^{4})

3 0.216 = 0.6

= (0.3 j - 0.6 k^{2}) (0.02 7^{\frac{2}{3}} j^{2} + 3 0.005832 j k^{2} + 0.21 6^{\frac{2}{3}} k^{4})

0.02 7^{\frac{2}{3}} = 0.09

= (0.3 j - 0.6 k^{2}) (0.09 j^{2} + 3 0.005832 j k^{2} + 0.21 6^{\frac{2}{3}} k^{4})

3 0.005832 = 0.18

= (0.3 j - 0.6 k^{2}) (0.09 j^{2} + 0.18 j k^{2} + 0.21 6^{\frac{2}{3}} k^{4})

0.21 6^{\frac{2}{3}} = 0.36

= (0.3 j - 0.6 k^{2}) (0.09 j^{2} + 0.18 j k^{2} + 0.36 k^{4})

f a c t or + x - 1 1^{3}

f a c t or (2 - x)^{2} + 3 (2 - x) - 4

f a c t or \frac{y}{2 x y + y ^{2}}

f a c t or (a - 3)^{2} (a + 3) (a + 3)

f a c t or 12 s x - 9 x t - 8 sy + 6 t y