erweitern ((2n^3)/6+(3n^2)/6+n/6)^2

Lösung

erweitern

(\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})^{2}

\frac{n ^{6} + n ^{4}}{9} + \frac{n ^{5}}{3} + \frac{n ^{4}}{4} + \frac{n ^{3}}{6} + \frac{n ^{2}}{36}

Schritte zur Lösung

(\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})^{2} = (\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6}) (\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})

= (\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6}) (\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})

Setze Klammern

= \frac{2 n ^{3}}{6} \cdot \frac{2 n ^{3}}{6} + \frac{2 n ^{3}}{6} \cdot \frac{3 n ^{2}}{6} + \frac{2 n ^{3}}{6} \cdot \frac{n}{6} + \frac{3 n ^{2}}{6} \cdot \frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} \cdot \frac{3 n ^{2}}{6} + \frac{3 n ^{2}}{6} \cdot \frac{n}{6} + \frac{n}{6} \cdot \frac{2 n ^{3}}{6} + \frac{n}{6} \cdot \frac{3 n ^{2}}{6} + \frac{n}{6} \cdot \frac{n}{6}

Vereinfache

\frac{2 n ^{3}}{6} \cdot \frac{2 n ^{3}}{6} + \frac{2 n ^{3}}{6} \cdot \frac{3 n ^{2}}{6} + \frac{2 n ^{3}}{6} \cdot \frac{n}{6} + \frac{3 n ^{2}}{6} \cdot \frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} \cdot \frac{3 n ^{2}}{6} + \frac{3 n ^{2}}{6} \cdot \frac{n}{6} + \frac{n}{6} \cdot \frac{2 n ^{3}}{6} + \frac{n}{6} \cdot \frac{3 n ^{2}}{6} + \frac{n}{6} \cdot \frac{n}{6} : \frac{n ^{6} + n ^{4}}{9} + \frac{n ^{5}}{3} + \frac{n ^{4}}{4} + \frac{n ^{3}}{6} + \frac{n ^{2}}{36}

= \frac{n ^{6} + n ^{4}}{9} + \frac{n ^{5}}{3} + \frac{n ^{4}}{4} + \frac{n ^{3}}{6} + \frac{n ^{2}}{36}

e x p an d \frac{2 ( 7 - 4 )}{3}

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e x p an d l {e^{4 t} (t - cos (t))}

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e x p an d - \frac{100}{( x + 1 ) ^{2}}