erweitern ((2x+x^3)^4)/(12)

Lösung

erweitern

\frac{( 2 x + x ^{3} ) ^{4}}{12}

\frac{x ^{12}}{12} + \frac{2 x ^{10}}{3} + 2 x^{8} + \frac{8 x ^{6}}{3} + \frac{4 x ^{4}}{3}

Schritte zur Lösung

\frac{( 2 x + x ^{3} ) ^{4}}{12}

(2 x + x^{3})^{4} = 16 x^{4} + 32 x^{6} + 24 x^{8} + 8 x^{10} + x^{12}

= \frac{16 x ^{4} + 32 x ^{6} + 24 x ^{8} + 8 x ^{10} + x ^{12}}{12}

Wende Bruchregel an:

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

\frac{16 x ^{4} + 32 x ^{6} + 24 x ^{8} + 8 x ^{10} + x ^{12}}{12} = \frac{16 x ^{4}}{12} + \frac{32 x ^{6}}{12} + \frac{24 x ^{8}}{12} + \frac{8 x ^{10}}{12} + \frac{x ^{12}}{12}

= \frac{16 x ^{4}}{12} + \frac{32 x ^{6}}{12} + \frac{24 x ^{8}}{12} + \frac{8 x ^{10}}{12} + \frac{x ^{12}}{12}

\frac{16 x ^{4}}{12} = \frac{4 x ^{4}}{3}

\frac{32 x ^{6}}{12} = \frac{8 x ^{6}}{3}

\frac{24 x ^{8}}{12} = 2 x^{8}

\frac{8 x ^{10}}{12} = \frac{2 x ^{10}}{3}

= \frac{4 x ^{4}}{3} + \frac{8 x ^{6}}{3} + 2 x^{8} + \frac{2 x ^{10}}{3} + \frac{x ^{12}}{12}

Rewrite in standard form

= \frac{x ^{12}}{12} + \frac{2 x ^{10}}{3} + 2 x^{8} + \frac{8 x ^{6}}{3} + \frac{4 x ^{4}}{3}

e x p an d \frac{3 3 x + 1}{x ( x - 2 )}

e x p an d 5.58 X 102

e x p an d 48 \cdot 25

e x p an d 2 x (2 - ln (x))

y = y - 1