< Polynom < Quadrat < 1 <
Aufgabe
Es ist
(
1
+
1
2
x
−
1
8
x
2
)
2
=
(
1
+
1
2
x
−
1
8
x
2
)
⋅
(
1
+
1
2
x
−
1
8
x
2
)
=
1
+
1
4
x
2
+
1
64
x
4
+
x
−
1
4
x
2
−
1
8
x
3
=
1
+
x
−
1
8
x
3
+
1
64
x
4
.
{\displaystyle {}{\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
This article is issued from
Wikiversity
. The text is licensed under
Creative Commons - Attribution - Sharealike
. Additional terms may apply for the media files.
