erweitern ((10x^2+9)^3)/(3375)

Lösung

erweitern

\frac{( 10 x ^{2} + 9 ) ^{3}}{3375}

\frac{8 x ^{6}}{27} + \frac{4 x ^{4}}{5} + \frac{18 x ^{2}}{25} + \frac{27}{125}

Schritte zur Lösung

\frac{( 10 x ^{2} + 9 ) ^{3}}{3375}

(10 x^{2} + 9)^{3} = 1000 x^{6} + 2700 x^{4} + 2430 x^{2} + 729

= \frac{1000 x ^{6} + 2700 x ^{4} + 2430 x ^{2} + 729}{3375}

Wende Bruchregel an:

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

\frac{1000 x ^{6} + 2700 x ^{4} + 2430 x ^{2} + 729}{3375} = \frac{1000 x ^{6}}{3375} + \frac{2700 x ^{4}}{3375} + \frac{2430 x ^{2}}{3375} + \frac{729}{3375}

= \frac{1000 x ^{6}}{3375} + \frac{2700 x ^{4}}{3375} + \frac{2430 x ^{2}}{3375} + \frac{729}{3375}

\frac{1000 x ^{6}}{3375} = \frac{8 x ^{6}}{27}

\frac{2700 x ^{4}}{3375} = \frac{4 x ^{4}}{5}

\frac{2430 x ^{2}}{3375} = \frac{18 x ^{2}}{25}

\frac{729}{3375} = \frac{27}{125}

= \frac{8 x ^{6}}{27} + \frac{4 x ^{4}}{5} + \frac{18 x ^{2}}{25} + \frac{27}{125}

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e x p an d cos^{2} (θ) - sin^{2} (θ)