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Zuletzt geändert von akukin am 2025/11/17 09:57
Von Version 5.2
bearbeitet von akukin
am 2025/11/17 09:57
Änderungskommentar: Update document after refactoring.
Auf Version 1.1
bearbeitet von akukin
am 2025/07/12 17:01
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Zusammenfassung

Details

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1 -Klasse 8.BPE_1.WebHome
1 +Klasse 8.BPE_1_1.WebHome
Inhalt
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1 1  Vereinfache:
2 -1.a)(((
2 +1.a)
3 +
3 3  {{formula}}
4 -\begin{align*}
5 -&\color{blue}{2(4a - 5) - 3(2a - 3) + 4(-3a + 5)} \\
5 +\begin{align}
6 +&\textcolor{blue!50!black}{2(4a - 5) - 3(2a - 3) + 4(-3a + 5)} \\
6 6  &= 8a - 10 - 6a + 9 - 12a + 20 = \textbf{-10a + 19}
7 -\end{align*}
8 +\end{align}
8 8  {{/formula}}
9 -)))
10 +
10 10  1.b)
11 11  
12 12  {{formula}}
13 -\begin{align*}
14 -&\color{blue}{x - (x + 3) - 4(-x + 1)}\\
14 +\begin{align}
15 +&\textcolor{blue!50!black}{x - (x + 3) - 4(-x + 1)}\\
15 15  &= x - x - 3 + 4x - 4 = \textbf{4x - 7}
16 -\end{align*}
17 +\end{align}
17 17  {{/formula}}
18 18  
19 19  2.a)
20 20  
21 21  {{formula}}
22 -\begin{align*}
23 -&\color{blue}{6a - 2(7b - (4a + 3b)) + 2((2a - b) - 7a)}\\
23 +\begin{align}
24 +&\textcolor{blue!50!black}{6a - 2(7b - (4a + 3b)) + 2((2a - b) - 7a)}\\
24 24  &= 6a - 2(7b - 4a - 3b) + 2(2a - b - 7a) \\
25 25  &= 6a - 14b + 8a + 6b + 4a - 2b - 14a = \textbf{4a - 10b}
26 -\end{align*}
27 +\end{align}
27 27  {{/formula}}
28 28  
29 29  2.b)
30 30  
31 31  {{formula}}
32 -\begin{align*}
33 -&\color{blue}{2x + 3(4 - (2x + 1) + 3x)}\\
33 +\begin{align}
34 +&\textcolor{blue!50!black}{2x + 3(4 - (2x + 1) + 3x)}\\
34 34  &= 2x + 3(4 - 2x - 1 + 3x)\\
35 35  &= 2x + 3(3 + x) = 2x + 9 + 3x = \textbf{5x + 9}
36 -\end{align*}
37 +\end{align}
37 37  {{/formula}}
38 38  
39 39  Multipliziere aus:
40 40  
41 -3.a) {{formula}}\color{blue}{(3a + b)(a - 5b)} = \mathbf{3a^2 - 14ab - 5b^2}{{/formula}}
42 +3.a) {{formula}}\textcolor{blue!50!black}{(3a + b)(a - 5b)} = \mathbf{3a^2 - 14ab - 5b^2}{{/formula}}
42 42  3.b) {{formula}}(4x - 3)(-x + \frac{1}{3})= \mathbf{-4x^2 + \frac{13}{3}x - 1}{{/formula}}
43 43  
44 -4.a) {{formula}}\color{blue}{(2x + y)^2}= \mathbf{4x^2 + 4xy + y^2}{{/formula}}
45 -4.b) {{formula}}\color{blue}{(x - 3y)^2}= \mathbf{x^2 - 6xy + 9y^2}{{/formula}}
46 -4.c) {{formula}}\color{blue}{(x^2 - 2)(x^2 + 2)}= \mathbf{x^4 - 4}{{/formula}}
45 +4.a) {{formula}}\textcolor{blue!50!black}{(2x + y)^2}= \mathbf{4x^2 + 4xy + y^2}{{/formula}}
46 +4.b) {{formula}}\textcolor{blue!50!black}{(x - 3y)^2}= \mathbf{x^2 - 6xy + 9y^2}{{/formula}}
47 +4.c) {{formula}}\textcolor{blue!50!black}{(x^2 - 2)(x^2 + 2)}= \mathbf{x^4 - 4}{{/formula}}
47 47  4.d)
48 48  
49 49  {{formula}}
50 -\begin{align*}
51 -&\color{blue}{(3 - x)^2 - (x + 1)^2 + 2(x - 1)(x + 1)}\\
51 +\begin{align}
52 +&\textcolor{blue!50!black}{(3 - x)^2 - (x + 1)^2 + 2(x - 1)(x + 1)}\\
52 52  &= (9 - 6x + x^2) - (x^2 + 2x + 1) + 2(x^2 - 1)\\
53 53  &= 9 - 6x + x^2 - x^2 - 2x - 1 + 2x^2 - 2 = \mathbf{2x^2 - 8x + 6}
54 -\end{align*}
55 +\end{align}
55 55  {{/formula}}
56 56  
57 57  Faktorisiere:
58 58  
59 -5.a) {{formula}}\color{blue}{12ax^2 - 8ax}= \mathbf{4ax(3x - 2)}{{/formula}}
60 -5.b) {{formula}}\color{blue}{3x^2 - 12}= 3(x^2 - 4) = \mathbf{3(x - 2)(x + 2)}{{/formula}}
61 -5.c) {{formula}}\color{blue}{\frac{3ax^2 - 3a}{9x + 9}}= \frac{3a(x^2 - 1)}{9(x + 1)} = \frac{a(x - 1)(x + 1)}{3(x + 1)} = \mathbf{\frac{a(x - 1)}{3}}{{/formula}}
60 +5.a) {{formula}}\textcolor{blue!50!black}{12ax^2 - 8ax}= \mathbf{4ax(3x - 2)}{{/formula}}
61 +5.b) {{formula}}\textcolor{blue!50!black}{3x^2 - 12}= 3(x^2 - 4) = \mathbf{3(x - 2)(x + 2)}{{/formula}}
62 +5.c) {{formula}}\textcolor{blue!50!black}{\frac{3ax^2 - 3a}{9x + 9}}= \frac{3a(x^2 - 1)}{9(x + 1)} = \frac{3a(x - 1)(x + 1)}{9(x + 1)} = \mathbf{\frac{a(x - 1)}{3}}{{/formula}}