erweitern (((z+12))/2)^3

Lösung

erweitern

(\frac{( z + 12 )}{2})^{3}

\frac{z ^{3}}{8} + \frac{9 z ^{2}}{2} + 54 z + 216

Schritte zur Lösung

(\frac{z + 12}{2})^{3}

Wende Exponentenregel an:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( z + 12 ) ^{3}}{2 ^{3}}

(z + 12)^{3} = z^{3} + 36 z^{2} + 432 z + 1728

= \frac{z ^{3} + 36 z ^{2} + 432 z + 1728}{2 ^{3}}

2^{3} = 8

= \frac{z ^{3} + 36 z ^{2} + 432 z + 1728}{8}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{z ^{3} + 36 z ^{2} + 432 z + 1728}{8} = \frac{z ^{3}}{8} + \frac{36 z ^{2}}{8} + \frac{432 z}{8} + \frac{1728}{8}

= \frac{z ^{3}}{8} + \frac{36 z ^{2}}{8} + \frac{432 z}{8} + \frac{1728}{8}

Streiche

\frac{36 z ^{2}}{8} : \frac{9 z ^{2}}{2}

= \frac{z ^{3}}{8} + \frac{9 z ^{2}}{2} + \frac{432 z}{8} + \frac{1728}{8}

Teile die Zahlen:

\frac{432}{8} = 54

= \frac{z ^{3}}{8} + \frac{9 z ^{2}}{2} + 54 z + \frac{1728}{8}

Teile die Zahlen:

\frac{1728}{8} = 216

= \frac{z ^{3}}{8} + \frac{9 z ^{2}}{2} + 54 z + 216

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