erweitern ((8b+9)^3)/(1728)

Lösung

erweitern

\frac{( 8 b + 9 ) ^{3}}{1728}

\frac{8 b ^{3}}{27} + b^{2} + \frac{9 b}{8} + \frac{27}{64}

Schritte zur Lösung

\frac{( 8 b + 9 ) ^{3}}{1728}

(8 b + 9)^{3} = 512 b^{3} + 1728 b^{2} + 1944 b + 729

= \frac{512 b ^{3} + 1728 b ^{2} + 1944 b + 729}{1728}

Wende Bruchregel an:

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

\frac{512 b ^{3} + 1728 b ^{2} + 1944 b + 729}{1728} = \frac{512 b ^{3}}{1728} + \frac{1728 b ^{2}}{1728} + \frac{1944 b}{1728} + \frac{729}{1728}

= \frac{512 b ^{3}}{1728} + \frac{1728 b ^{2}}{1728} + \frac{1944 b}{1728} + \frac{729}{1728}

\frac{512 b ^{3}}{1728} = \frac{8 b ^{3}}{27}

\frac{1728 b ^{2}}{1728} = b^{2}

\frac{1944 b}{1728} = \frac{9 b}{8}

\frac{729}{1728} = \frac{27}{64}

= \frac{8 b ^{3}}{27} + b^{2} + \frac{9 b}{8} + \frac{27}{64}

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