erweitern ((3sqrt(x)+2)^6)/9

Lösung

erweitern

\frac{( 3 x + 2 ) ^{6}}{9}

81 x^{3} + 324 x^{\frac{5}{2}} + 540 x^{2} + 480 x^{\frac{3}{2}} + 240 x + 64 x + \frac{64}{9}

Schritte zur Lösung

\frac{( 3 x + 2 ) ^{6}}{9}

(3 x + 2)^{6} = 729 x^{3} + 2916 x^{\frac{5}{2}} + 4860 x^{2} + 4320 x^{\frac{3}{2}} + 2160 x + 576 x + 64

= \frac{729 x ^{3} + 2916 x ^{\frac{5}{2}} + 4860 x ^{2} + 4320 x ^{\frac{3}{2}} + 2160 x + 576 x + 64}{9}

Wende Bruchregel an:

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

\frac{729 x ^{3} + 2916 x ^{\frac{5}{2}} + 4860 x ^{2} + 4320 x ^{\frac{3}{2}} + 2160 x + 576 x + 64}{9} = \frac{729 x ^{3}}{9} + \frac{2916 x ^{\frac{5}{2}}}{9} + \frac{4860 x ^{2}}{9} + \frac{4320 x ^{\frac{3}{2}}}{9} + \frac{2160 x}{9} + \frac{576 x}{9} + \frac{64}{9}

= \frac{729 x ^{3}}{9} + \frac{2916 x ^{\frac{5}{2}}}{9} + \frac{4860 x ^{2}}{9} + \frac{4320 x ^{\frac{3}{2}}}{9} + \frac{2160 x}{9} + \frac{576 x}{9} + \frac{64}{9}

\frac{729 x ^{3}}{9} = 81 x^{3}

\frac{2916 x ^{\frac{5}{2}}}{9} = 324 x^{\frac{5}{2}}

\frac{4860 x ^{2}}{9} = 540 x^{2}

\frac{4320 x ^{\frac{3}{2}}}{9} = 480 x^{\frac{3}{2}}

\frac{2160 x}{9} = 240 x

\frac{576 x}{9} = 64 x

= 81 x^{3} + 324 x^{\frac{5}{2}} + 540 x^{2} + 480 x^{\frac{3}{2}} + 240 x + 64 x + \frac{64}{9}

e x p an d \frac{x ( 3 x ^{2} - 1 )}{1 - x ^{4}}

e x p an d e^{t (x - y)}

e x p an d \frac{d t}{( 1 - 6 t ) ^{4}}

e x p an d \frac{( 3 x - 1 ) ( x + 1 )}{x ( x - 4 )}

e x p an d - \frac{6 ( 4 161 - 21 )}{61}