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Berechne:
= z^3 + 3z^2\cdot\frac{8}{3} + 3z\cdot\frac{64}{9} + \frac{512}{27} - 8\left(z^2 + \frac{16}{3}z + \frac{64}{9}\right) + 9z + 24 - 18
= z^3 + 8z^2 + 21.333z + 18.96 - 8z^2 - \frac{128}{3}z - \frac{512}{9} + 9z + 6
Bessere Zahlen:
\( \frac{8}{3} \), \( (\frac{8}{3})^2 = \frac{64}{9} \), \( (\frac{8}{3})^3 = \frac{512}{27} \)
Jede Term:
\( (z + \frac{8}{3})^3 = z^3 + 3\cdot\frac{8}{3}z^2 + 3\cdot\frac{64}{9}z + \frac{512}{27} = z^3 + 8z^2 + \frac{192}{9}z + \frac{512}{27} = z^3 + 8z^2 + \frac{64}{3}z + \frac{512}{27} \)
\( -8(z + \frac{8}{3})^2 = -8(z^2 + \frac{16}{3}z + \frac{64}{9}) = -8z^2 - \frac{128}{3}z - \frac{512}{9} \)
\( 9(z + \frac{8}{3}) = 9z + 24 \)
Summe: