erweitern ((3x^8+1)^{3/2}(9x^8-2))/(540)

Lösung

erweitern

\frac{( 3 x ^{8} + 1 ) ^{\frac{3}{2}} ( 9 x ^{8} - 2 )}{540}

\frac{x ^{8} ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{60} - \frac{( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{270}

Schritte zur Lösung

\frac{( 3 x ^{8} + 1 ) ^{\frac{3}{2}} ( 9 x ^{8} - 2 )}{540}

Multipliziere aus

(3 x^{8} + 1)^{\frac{3}{2}} (9 x^{8} - 2) : 9 x^{8} (3 x^{8} + 1)^{\frac{3}{2}} - 2 (3 x^{8} + 1)^{\frac{3}{2}}

= \frac{9 x ^{8} ( 3 x ^{8} + 1 ) ^{\frac{3}{2}} - 2 ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{540}

Wende Bruchregel an:

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

\frac{9 x ^{8} ( 3 x ^{8} + 1 ) ^{\frac{3}{2}} - 2 ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{540} = \frac{9 x ^{8} ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{540} - \frac{2 ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{540}

= \frac{9 x ^{8} ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{540} - \frac{2 ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{540}

Streiche

\frac{9 x ^{8} ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{540} : \frac{x ^{8} ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{60}

= \frac{x ^{8} ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{60} - \frac{2 ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{540}

Streiche

\frac{2 ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{540} : \frac{( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{270}

= \frac{x ^{8} ( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{60} - \frac{( 3 x ^{8} + 1 ) ^{\frac{3}{2}}}{270}

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