Wiki-Quellcode von Lösung Termumformungen
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author | version | line-number | content |
---|---|---|---|
1 | Vereinfache: | ||
2 | 1.a) | ||
3 | |||
4 | {{formula}} | ||
5 | \begin{align*} | ||
6 | &\color{blue}{2(4a - 5) - 3(2a - 3) + 4(-3a + 5)} \\ | ||
7 | &= 8a - 10 - 6a + 9 - 12a + 20 = \textbf{-10a + 19} | ||
8 | \end{align*} | ||
9 | {{/formula}} | ||
10 | |||
11 | 1.b) | ||
12 | |||
13 | {{formula}} | ||
14 | \begin{align*} | ||
15 | &\color{blue}{x - (x + 3) - 4(-x + 1)}\\ | ||
16 | &= x - x - 3 + 4x - 4 = \textbf{4x - 7} | ||
17 | \end{align*} | ||
18 | {{/formula}} | ||
19 | |||
20 | 2.a) | ||
21 | |||
22 | {{formula}} | ||
23 | \begin{align*} | ||
24 | &\color{blue}{6a - 2(7b - (4a + 3b)) + 2((2a - b) - 7a)}\\ | ||
25 | &= 6a - 2(7b - 4a - 3b) + 2(2a - b - 7a) \\ | ||
26 | &= 6a - 14b + 8a + 6b + 4a - 2b - 14a = \textbf{4a - 10b} | ||
27 | \end{align*} | ||
28 | {{/formula}} | ||
29 | |||
30 | 2.b) | ||
31 | |||
32 | {{formula}} | ||
33 | \begin{align*} | ||
34 | &\color{blue}{2x + 3(4 - (2x + 1) + 3x)}\\ | ||
35 | &= 2x + 3(4 - 2x - 1 + 3x)\\ | ||
36 | &= 2x + 3(3 + x) = 2x + 9 + 3x = \textbf{5x + 9} | ||
37 | \end{align*} | ||
38 | {{/formula}} | ||
39 | |||
40 | Multipliziere aus: | ||
41 | |||
42 | 3.a) {{formula}}\color{blue}{(3a + b)(a - 5b)} = \mathbf{3a^2 - 14ab - 5b^2}{{/formula}} | ||
43 | 3.b) {{formula}}(4x - 3)(-x + \frac{1}{3})= \mathbf{-4x^2 + \frac{13}{3}x - 1}{{/formula}} | ||
44 | |||
45 | 4.a) {{formula}}\color{blue}{(2x + y)^2}= \mathbf{4x^2 + 4xy + y^2}{{/formula}} | ||
46 | 4.b) {{formula}}\color{blue}{(x - 3y)^2}= \mathbf{x^2 - 6xy + 9y^2}{{/formula}} | ||
47 | 4.c) {{formula}}\color{blue}{(x^2 - 2)(x^2 + 2)}= \mathbf{x^4 - 4}{{/formula}} | ||
48 | 4.d) | ||
49 | |||
50 | {{formula}} | ||
51 | \begin{align*} | ||
52 | &\color{blue}{(3 - x)^2 - (x + 1)^2 + 2(x - 1)(x + 1)}\\ | ||
53 | &= (9 - 6x + x^2) - (x^2 + 2x + 1) + 2(x^2 - 1)\\ | ||
54 | &= 9 - 6x + x^2 - x^2 - 2x - 1 + 2x^2 - 2 = \mathbf{2x^2 - 8x + 6} | ||
55 | \end{align*} | ||
56 | {{/formula}} | ||
57 | |||
58 | Faktorisiere: | ||
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{a(x - 1)(x + 1)}{3(x + 1)} = \mathbf{\frac{a(x - 1)}{3}}{{/formula}} |