Änderungen von Dokument Lösung Termumformungen

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• Seiteneigenschaften (1 geändert, 0 hinzugefügt, 0 gelöscht)

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...	...	@@ -2,57 +2,57 @@
2	2	1.a)
3	3
4	4	{{formula}}
5		-\begin{align}
6		-&\textcolor{blue!50!black}{2(4a - 5) - 3(2a - 3) + 4(-3a + 5)} \\
	5	+\begin{align*}
	6	+&\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}
	8	+\end{align*}
9	9	{{/formula}}
10	10
11	11	1.b)
12	12
13	13	{{formula}}
14		-\begin{align}
15		-&\textcolor{blue!50!black}{x - (x + 3) - 4(-x + 1)}\\
	14	+\begin{align*}
	15	+&\color{blue}{x - (x + 3) - 4(-x + 1)}\\
16	16	&= x - x - 3 + 4x - 4 = \textbf{4x - 7}
17		-\end{align}
	17	+\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)}\\
	23	+\begin{align*}
	24	+&\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}
	27	+\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)}\\
	33	+\begin{align*}
	34	+&\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}
	37	+\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}}
	42	+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}}
	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	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)}\\
	51	+\begin{align*}
	52	+&\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}
	55	+\end{align*}
56	56	{{/formula}}
57	57
58	58	Faktorisiere: