faktorisieren 0.064x^{27}-1.331b^{15}

Lösung

faktorisieren

0.064 x^{27} - 1.331 b^{15}

(0.4 x^{9} - 1.1 b^{5}) (0.16 x^{18} + 0.44 b^{5} x^{9} + 1.21 b^{10})

Schritte zur Lösung

0.064 x^{27} - 1.331 b^{15}

Schreibe

0.064 x^{27} - 1.331 b^{15}

um:

(3 0.064 x^{9})^{3} - (3 1.331 b^{5})^{3}

= (3 0.064 x^{9})^{3} - (3 1.331 b^{5})^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(3 0.064 x^{9})^{3} - (3 1.331 b^{5})^{3} = (3 0.064 x^{9} - 3 1.331 b^{5}) ((3 0.064)^{2} x^{18} + 3 0.064 3 1.331 x^{9} b^{5} + (3 1.331)^{2} b^{10})

= (3 0.064 x^{9} - 3 1.331 b^{5}) ((3 0.064)^{2} x^{18} + 3 0.064 3 1.331 x^{9} b^{5} + (3 1.331)^{2} b^{10})

Fasse zusammen

= (3 0.064 x^{9} - 3 1.331 b^{5}) (0.06 4^{\frac{2}{3}} x^{18} + 3 0.085184 x^{9} b^{5} + 1.33 1^{\frac{2}{3}} b^{10})

3 0.064 = 0.4

= (0.4 x^{9} - 3 1.331 b^{5}) (0.06 4^{\frac{2}{3}} x^{18} + 3 0.085184 b^{5} x^{9} + 1.33 1^{\frac{2}{3}} b^{10})

3 1.331 = 1.1

= (0.4 x^{9} - 1.1 b^{5}) (0.06 4^{\frac{2}{3}} x^{18} + 3 0.085184 b^{5} x^{9} + 1.33 1^{\frac{2}{3}} b^{10})

0.06 4^{\frac{2}{3}} = 0.16

= (0.4 x^{9} - 1.1 b^{5}) (0.16 x^{18} + 3 0.085184 b^{5} x^{9} + 1.33 1^{\frac{2}{3}} b^{10})

3 0.085184 = 0.44

= (0.4 x^{9} - 1.1 b^{5}) (0.16 x^{18} + 0.44 b^{5} x^{9} + 1.33 1^{\frac{2}{3}} b^{10})

1.33 1^{\frac{2}{3}} = 1.21

= (0.4 x^{9} - 1.1 b^{5}) (0.16 x^{18} + 0.44 b^{5} x^{9} + 1.21 b^{10})

\frac{d}{d t} ((x) (t cos (t)))

f a c t or 3 a^{2} - 9 ab - 5 a c + 15 b c

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

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

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