erweitern (x-9/2)^3

Lösung

erweitern

(x - \frac{9}{2})^{3}

\frac{8 x ^{3} + 486 x - 108 x ^{2} - 729}{8}

Schritte zur Lösung

(x - \frac{9}{2})^{3}

Wende Formel für perfekte dritte Potenzen an:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(x - \frac{9}{2})^{3} = x^{3} - 3 x^{2} \frac{9}{2} + 3 x (\frac{9}{2})^{2} - (\frac{9}{2})^{3}

= x^{3} - 3 x^{2} \frac{9}{2} + 3 x (\frac{9}{2})^{2} - (\frac{9}{2})^{3}

Vereinfache

x^{3} - 3 x^{2} \frac{9}{2} + 3 x (\frac{9}{2})^{2} - (\frac{9}{2})^{3} : \frac{8 x ^{3} + 486 x - 108 x ^{2} - 729}{8}

= \frac{8 x ^{3} + 486 x - 108 x ^{2} - 729}{8}

e x p an d A (8, - 9)

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e x p an d (3 y + 2) (3 x^{\frac{3}{2}} + 2 x^{\frac{1}{2}})

e x p an d sin ((π - 1) n)