erweitern (4(x+6)^5)/(sqrt(x^3))

Lösung

erweitern

\frac{4 ( x + 6 ) ^{5}}{x ^{3}}

\frac{x ( 4 x ^{5} + 120 x ^{4} + 1440 x ^{3} + 8640 x ^{2} + 25920 x + 31104 )}{x ^{2}}

Schritte zur Lösung

\frac{4 ( x + 6 ) ^{5}}{x ^{3}}

x^{3} = x x

= \frac{4 ( x + 6 ) ^{5}}{x x}

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

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

Multipliziere aus

4 (x^{5} + 30 x^{4} + 360 x^{3} + 2160 x^{2} + 6480 x + 7776) : 4 x^{5} + 120 x^{4} + 1440 x^{3} + 8640 x^{2} + 25920 x + 31104

= \frac{4 x ^{5} + 120 x ^{4} + 1440 x ^{3} + 8640 x ^{2} + 25920 x + 31104}{x x}

Rationalisiere

\frac{4 x ^{5} + 120 x ^{4} + 1440 x ^{3} + 8640 x ^{2} + 25920 x + 31104}{x x} : \frac{x ( 4 x ^{5} + 120 x ^{4} + 1440 x ^{3} + 8640 x ^{2} + 25920 x + 31104 )}{x ^{2}}

= \frac{x ( 4 x ^{5} + 120 x ^{4} + 1440 x ^{3} + 8640 x ^{2} + 25920 x + 31104 )}{x ^{2}}

e x p an d 5 (8 + 36)

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

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

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

e x p an d \frac{( 3 n + 4 ) ^{2}}{9}