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

Lösung

erweitern

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

x^{2} + x^{3} + \frac{11 x ^{4}}{12} + \frac{x ^{5}}{6} + \frac{x ^{5}}{6} + \frac{x ^{6}}{9}

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3})^{2} = (x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3}) (x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3})

= (x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3}) (x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3})

Setze Klammern

= xx + x \frac{x ^{2}}{2} + x \frac{x ^{3}}{3} + \frac{x ^{2}}{2} x + \frac{x ^{2}}{2} \cdot \frac{x ^{2}}{2} + \frac{x ^{2}}{2} \cdot \frac{x ^{3}}{3} + \frac{x ^{3}}{3} x + \frac{x ^{3}}{3} \cdot \frac{x ^{2}}{2} + \frac{x ^{3}}{3} \cdot \frac{x ^{3}}{3}

Vereinfache

xx + x \frac{x ^{2}}{2} + x \frac{x ^{3}}{3} + \frac{x ^{2}}{2} x + \frac{x ^{2}}{2} \cdot \frac{x ^{2}}{2} + \frac{x ^{2}}{2} \cdot \frac{x ^{3}}{3} + \frac{x ^{3}}{3} x + \frac{x ^{3}}{3} \cdot \frac{x ^{2}}{2} + \frac{x ^{3}}{3} \cdot \frac{x ^{3}}{3} : x^{2} + x^{3} + \frac{11 x ^{4}}{12} + \frac{x ^{5}}{6} + \frac{x ^{5}}{6} + \frac{x ^{6}}{9}

= x^{2} + x^{3} + \frac{11 x ^{4}}{12} + \frac{x ^{5}}{6} + \frac{x ^{5}}{6} + \frac{x ^{6}}{9}

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

e x p an d \frac{1}{2} (5 ln (5) - 4)

e x p an d (x + \frac{2}{x ^{2}})^{15}

e x p an d (\frac{6}{7} - x)^{3}

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