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Zuletzt geändert von akukin am 2025/11/17 09:57
Von Version 1.1
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Auf Version 5.2
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am 2025/11/17 09:57
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Zusammenfassung

Details

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