erweitern ((sqrt(a)-sqrt(x))^5)/5

Lösung

erweitern

\frac{( a - x ) ^{5}}{5}

\frac{a ^{\frac{5}{2}}}{5} - a^{2} x + 2 a^{\frac{3}{2}} x - 2 a x^{\frac{3}{2}} + a x^{2} - \frac{x ^{\frac{5}{2}}}{5}

Schritte zur Lösung

\frac{( a - x ) ^{5}}{5}

(a - x)^{5} = a^{\frac{5}{2}} - 5 a^{2} x + 10 a^{\frac{3}{2}} x - 10 a x^{\frac{3}{2}} + 5 a x^{2} - x^{\frac{5}{2}}

= \frac{a ^{\frac{5}{2}} - 5 a ^{2} x + 10 a ^{\frac{3}{2}} x - 10 a x ^{\frac{3}{2}} + 5 a x ^{2} - x ^{\frac{5}{2}}}{5}

Wende Bruchregel an:

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

\frac{a ^{\frac{5}{2}} - 5 a ^{2} x + 10 a ^{\frac{3}{2}} x - 10 a x ^{\frac{3}{2}} + 5 a x ^{2} - x ^{\frac{5}{2}}}{5} = \frac{a ^{\frac{5}{2}}}{5} - \frac{5 a ^{2} x}{5} + \frac{10 a ^{\frac{3}{2}} x}{5} - \frac{10 a x ^{\frac{3}{2}}}{5} + \frac{5 a x ^{2}}{5} - \frac{x ^{\frac{5}{2}}}{5}

= \frac{a ^{\frac{5}{2}}}{5} - \frac{5 a ^{2} x}{5} + \frac{10 a ^{\frac{3}{2}} x}{5} - \frac{10 a x ^{\frac{3}{2}}}{5} + \frac{5 a x ^{2}}{5} - \frac{x ^{\frac{5}{2}}}{5}

\frac{5 a ^{2} x}{5} = a^{2} x

\frac{10 a ^{\frac{3}{2}} x}{5} = 2 a^{\frac{3}{2}} x

\frac{10 a x ^{\frac{3}{2}}}{5} = 2 a x^{\frac{3}{2}}

\frac{5 a x ^{2}}{5} = a x^{2}

= \frac{a ^{\frac{5}{2}}}{5} - a^{2} x + 2 a^{\frac{3}{2}} x - 2 a x^{\frac{3}{2}} + a x^{2} - \frac{x ^{\frac{5}{2}}}{5}

s im pl i f y 3 (3 + 22)

e x p an d \frac{\frac{d}{d x} ( t ^{2} + 9 )}{( 3 t - 6 ) ^{9}}

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

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

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