Wiki-Quellcode von Lösung Termumformungen
Zuletzt geändert von akukin am 2025/08/15 14:28
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| author | version | line-number | content |
|---|---|---|---|
| 1 | Vereinfache: | ||
| 2 | 1.a)((( | ||
| 3 | {{formula}} | ||
| 4 | \begin{align*} | ||
| 5 | &\color{blue}{2(4a - 5) - 3(2a - 3) + 4(-3a + 5)} \\ | ||
| 6 | &= 8a - 10 - 6a + 9 - 12a + 20 = \textbf{-10a + 19} | ||
| 7 | \end{align*} | ||
| 8 | {{/formula}} | ||
| 9 | ))) | ||
| 10 | 1.b) | ||
| 11 | |||
| 12 | {{formula}} | ||
| 13 | \begin{align*} | ||
| 14 | &\color{blue}{x - (x + 3) - 4(-x + 1)}\\ | ||
| 15 | &= x - x - 3 + 4x - 4 = \textbf{4x - 7} | ||
| 16 | \end{align*} | ||
| 17 | {{/formula}} | ||
| 18 | |||
| 19 | 2.a) | ||
| 20 | |||
| 21 | {{formula}} | ||
| 22 | \begin{align*} | ||
| 23 | &\color{blue}{6a - 2(7b - (4a + 3b)) + 2((2a - b) - 7a)}\\ | ||
| 24 | &= 6a - 2(7b - 4a - 3b) + 2(2a - b - 7a) \\ | ||
| 25 | &= 6a - 14b + 8a + 6b + 4a - 2b - 14a = \textbf{4a - 10b} | ||
| 26 | \end{align*} | ||
| 27 | {{/formula}} | ||
| 28 | |||
| 29 | 2.b) | ||
| 30 | |||
| 31 | {{formula}} | ||
| 32 | \begin{align*} | ||
| 33 | &\color{blue}{2x + 3(4 - (2x + 1) + 3x)}\\ | ||
| 34 | &= 2x + 3(4 - 2x - 1 + 3x)\\ | ||
| 35 | &= 2x + 3(3 + x) = 2x + 9 + 3x = \textbf{5x + 9} | ||
| 36 | \end{align*} | ||
| 37 | {{/formula}} | ||
| 38 | |||
| 39 | Multipliziere aus: | ||
| 40 | |||
| 41 | 3.a) {{formula}}\color{blue}{(3a + b)(a - 5b)} = \mathbf{3a^2 - 14ab - 5b^2}{{/formula}} | ||
| 42 | 3.b) {{formula}}(4x - 3)(-x + \frac{1}{3})= \mathbf{-4x^2 + \frac{13}{3}x - 1}{{/formula}} | ||
| 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}} | ||
| 47 | 4.d) | ||
| 48 | |||
| 49 | {{formula}} | ||
| 50 | \begin{align*} | ||
| 51 | &\color{blue}{(3 - x)^2 - (x + 1)^2 + 2(x - 1)(x + 1)}\\ | ||
| 52 | &= (9 - 6x + x^2) - (x^2 + 2x + 1) + 2(x^2 - 1)\\ | ||
| 53 | &= 9 - 6x + x^2 - x^2 - 2x - 1 + 2x^2 - 2 = \mathbf{2x^2 - 8x + 6} | ||
| 54 | \end{align*} | ||
| 55 | {{/formula}} | ||
| 56 | |||
| 57 | Faktorisiere: | ||
| 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}} |