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Lösung Termumformungen

Zuletzt geändert von akukin am 2025/07/12 19:03

Vereinfache:
1.a)

\begin{align} &\textcolor{blue!50!black}{2(4a - 5) - 3(2a - 3) + 4(-3a + 5)} \\ &= 8a - 10 - 6a + 9 - 12a + 20 = \textbf{-10a + 19} \end{align}

1.b)

\begin{align} &\textcolor{blue!50!black}{x - (x + 3) - 4(-x + 1)}\\ &= x - x - 3 + 4x - 4 = \textbf{4x - 7} \end{align}

2.a)

\begin{align} &\textcolor{blue!50!black}{6a - 2(7b - (4a + 3b)) + 2((2a - b) - 7a)}\\ &= 6a - 2(7b - 4a - 3b) + 2(2a - b - 7a) \\ &= 6a - 14b + 8a + 6b + 4a - 2b - 14a = \textbf{4a - 10b} \end{align}

2.b)

\begin{align} &\textcolor{blue!50!black}{2x + 3(4 - (2x + 1) + 3x)}\\ &= 2x + 3(4 - 2x - 1 + 3x)\\ &= 2x + 3(3 + x) = 2x + 9 + 3x = \textbf{5x + 9} \end{align}

Multipliziere aus:

3.a) \textcolor{blue!50!black}{(3a + b)(a - 5b)} = \mathbf{3a^2 - 14ab - 5b^2}
3.b) (4x - 3)(-x + \frac{1}{3})= \mathbf{-4x^2 + \frac{13}{3}x - 1}

4.a) \textcolor{blue!50!black}{(2x + y)^2}= \mathbf{4x^2 + 4xy + y^2}
4.b) \textcolor{blue!50!black}{(x - 3y)^2}= \mathbf{x^2 - 6xy + 9y^2}
4.c) \textcolor{blue!50!black}{(x^2 - 2)(x^2 + 2)}= \mathbf{x^4 - 4}
4.d)

\begin{align} &\textcolor{blue!50!black}{(3 - x)^2 - (x + 1)^2 + 2(x - 1)(x + 1)}\\ &= (9 - 6x + x^2) - (x^2 + 2x + 1) + 2(x^2 - 1)\\ &= 9 - 6x + x^2 - x^2 - 2x - 1 + 2x^2 - 2 = \mathbf{2x^2 - 8x + 6} \end{align}

Faktorisiere:

5.a) \textcolor{blue!50!black}{12ax^2 - 8ax}= \mathbf{4ax(3x - 2)}
5.b) \textcolor{blue!50!black}{3x^2 - 12}= 3(x^2 - 4) = \mathbf{3(x - 2)(x + 2)}
5.c) \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}}