Polynom/Quadrat/1/Aufgabe/Lösung

Es ist

${}{\begin{aligned}{\left(1+{\frac {1}{2}}x-{\frac {1}{8}}x^{2}\right)}^{2}&={\left(1+{\frac {1}{2}}x-{\frac {1}{8}}x^{2}\right)}\cdot {\left(1+{\frac {1}{2}}x-{\frac {1}{8}}x^{2}\right)}\\&=1+{\frac {1}{4}}x^{2}+{\frac {1}{64}}x^{4}+x-{\frac {1}{4}}x^{2}-{\frac {1}{8}}x^{3}\\&=1+x-{\frac {1}{8}}x^{3}+{\frac {1}{64}}x^{4}.\end{aligned}}$

Zur gelösten Aufgabe