erweitern ((1+6x)^5)/5

Lösung

erweitern

\frac{( 1 + 6 x ) ^{5}}{5}

\frac{7776 x ^{5}}{5} + 1296 x^{4} + 432 x^{3} + 72 x^{2} + 6 x + \frac{1}{5}

Schritte zur Lösung

\frac{( 1 + 6 x ) ^{5}}{5}

(1 + 6 x)^{5} = 1 + 30 x + 360 x^{2} + 2160 x^{3} + 6480 x^{4} + 7776 x^{5}

= \frac{1 + 30 x + 360 x ^{2} + 2160 x ^{3} + 6480 x ^{4} + 7776 x ^{5}}{5}

Wende Bruchregel an:

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

\frac{1 + 30 x + 360 x ^{2} + 2160 x ^{3} + 6480 x ^{4} + 7776 x ^{5}}{5} = \frac{1}{5} + \frac{30 x}{5} + \frac{360 x ^{2}}{5} + \frac{2160 x ^{3}}{5} + \frac{6480 x ^{4}}{5} + \frac{7776 x ^{5}}{5}

= \frac{1}{5} + \frac{30 x}{5} + \frac{360 x ^{2}}{5} + \frac{2160 x ^{3}}{5} + \frac{6480 x ^{4}}{5} + \frac{7776 x ^{5}}{5}

\frac{30 x}{5} = 6 x

\frac{360 x ^{2}}{5} = 72 x^{2}

\frac{2160 x ^{3}}{5} = 432 x^{3}

\frac{6480 x ^{4}}{5} = 1296 x^{4}

= \frac{1}{5} + 6 x + 72 x^{2} + 432 x^{3} + 1296 x^{4} + \frac{7776 x ^{5}}{5}

Rewrite in standard form

= \frac{7776 x ^{5}}{5} + 1296 x^{4} + 432 x^{3} + 72 x^{2} + 6 x + \frac{1}{5}

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

e x p an d 2 (ln (2 x) + β)

e x p an d \frac{2 s ( e ^{- π s} - e ^{- 2 π s} )}{s ^{2} + 4}

e x p an d \frac{1}{( 5 x + 2 ) ^{3}}

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