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Hallo!
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4
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6
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4
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{\displaystyle (a\pm b)^{4}=a^{4}\pm 4a^{3}b+6a^{2}b^{2}\pm 4ab^{3}+b^{4}}
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20
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20
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{\displaystyle -(5\cdot a-(20\cdot b+4\cdot c))=-5\cdot a+20\cdot b+4\cdot c}
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{\displaystyle a\cdot (b+c)=a\cdot b+a\cdot c}
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25
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{\displaystyle ({\frac {1}{-5}}\cdot a)^{2}\;=\;{\frac {1}{25}}\cdot a^{2}}
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4
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10
300
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{\displaystyle {\frac {1}{25}}\cdot {\frac {2}{3}}\cdot {\frac {5}{4}}\;=\;{\frac {10}{300}}\;=\;{\frac {1}{30}}}
26
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52
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13
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26
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0.5
{\displaystyle {\frac {26\cdot x^{5}+52\cdot x^{3}-13\cdot x^{2}}{-26\cdot x^{2}}}\;=\;-x^{3}-2\cdot x^{1}+0.5}
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{\displaystyle u_{1,2}={\frac {4\pm {\sqrt {16+16}}}{2}}}
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{\displaystyle x_{1,2,3,4}=\pm {\sqrt {u_{1,2}}}}
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{\displaystyle {\frac {a}{n}}\;+\;{\frac {b}{n}}\;=\;{\frac {a+b}{n}}}
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{\displaystyle {\frac {a}{n}}\;-\;{\frac {b}{n}}\;=\;{\frac {a-b}{n}}}
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{\displaystyle {\frac {a}{b}}\;\cdot \;n\;=\;{\frac {a\cdot n}{b}}}
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{\displaystyle {\frac {a}{b}}\;:\;n\;=\;{\frac {a}{b\cdot n}}}
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{\displaystyle {\frac {a}{b}}\;+\;{\frac {c}{d}}\;=\;{\frac {a\cdot d+c\cdot b}{b\cdot d}}}
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{\displaystyle {\frac {a}{b}}\;-\;{\frac {c}{d}}\;=\;{\frac {a\cdot d-c\cdot b}{b\cdot d}}}
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{\displaystyle {\frac {a}{b}}\;\cdot \;{\frac {c}{d}}\;=\;{\frac {a\cdot c}{b\cdot d}}}
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{\displaystyle {\frac {a}{b}}\;:\;{\frac {c}{d}}\;=\;{\frac {a}{b}}\;\cdot \;{\frac {d}{c}}\;=\;{\frac {a\cdot d}{b\cdot c}}}
Man dividiert also durch einen Bruch, indem man mit dem Kehrwert des Bruches multipliziert. Die Division wird also auf die Multiplikation zurückgeführt.
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{\displaystyle {\frac {a^{n}}{b^{m}}}=a^{n}\cdot b^{-m}}
--> Beispiel:
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1
{\displaystyle {\frac {3}{2}}=3\cdot 2^{-1}}
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{\displaystyle {\frac {a^{n}}{a^{m}}}=a^{n-m}}
--> Beispiel:
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3
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x
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2
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x
{\displaystyle {\frac {x^{3}}{x^{2}}}=x^{3}\cdot x^{-2}=x^{3-2}=x}
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{\displaystyle {\frac {a^{n}}{b^{n}}}=\left({\frac {a}{b}}\right)^{n}}
--> Beispiel:
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{\displaystyle {\frac {3^{2}}{2^{2}}}=\left({\frac {3}{2}}\right)^{2}}