• Ausmultiplizieren (1)
  • MNWeG
  • 13.05.2022
  • Mathematik
  • Gleichungen
  • M (Mindeststandard)
  • 7
  • Arbeitsblatt
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1
Vereinfache folgende Terme.
Denke daran, bei einem Faktor immer zuerst die Zahl und danach die Variablen in alphabetischer Reihenfolge zu schreiben.

Anstatt x5b=x5b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} x\cdot 5\cdot b=x5b solltest du also schreiben: x5b=5bx\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} x\cdot 5\cdot b=5bx
a(5+b)=a5+ab=5a+ab\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} a\cdot(5+b) &= a\cdot 5 + a\cdot b\\ &=5a+ab \end{aligned}

Beispiel:

a)   3(2+a)=32+3a=6+3a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} a)\ \ \ 3\cdot(2+a) &= \cloze{3\cdot 2 + 3\cdot a}\\ &=\cloze{6+3a} \end{aligned}
b)   4(x2)=4x42=4x8\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} b)\ \ \ 4\cdot(x-2) &= \cloze{4\cdot x - 4\cdot 2}\\ &=\cloze{4x-8} \end{aligned}
c)   3s(4+r)=3s4+3sr=12s+3rs\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} c)\ \ \ 3s\cdot(4+r) &= \cloze{3s\cdot 4 + 3s\cdot r}\\ &=\cloze{12s+3rs} \end{aligned}
d)   (x2a)5=5x52a=5x10a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} d)\ \ \ (x-2a)\cdot 5 &= \cloze{5\cdot x - 5\cdot 2a}\\ &=\cloze{5x-10a} \end{aligned}
e)   8f(f2f)=8ff8f2f=8f²16f²=8f²\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} e)\ \ \ 8f\cdot(f-2f) &= \cloze{8f\cdot f - 8f\cdot 2f}\\ &=\cloze{8f²-16f²}\\ &=\cloze{-8f²}\\ \end{aligned}
f)   (3a7b)2b=2b3a2b7b=6ab14b2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} f)\ \ \ (3a-7b)\cdot 2b &= \cloze{2b\cdot 3a - 2b\cdot 7b}\\ &=\cloze{6ab-14b^2} \end{aligned}
g)   20c(c4d)=20cc20c4d=20c²80cd\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} g)\ \ \ 20c\cdot(c-4d) &= \cloze{20c\cdot c- 20c\cdot 4d}\\ &=\cloze{20c²-80cd} \end{aligned}
h)   (3w5z)5z=5z3w5z5z=5x10a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} h)\ \ \ (3w-5z)\cdot 5z &= \cloze{5z\cdot 3w - 5z\cdot 5z}\\ &=\cloze{5x-10a} \end{aligned}
i)   (t+3t)t=tt+t3t=t²+3t²=4t2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} i)\ \ \ (t+3t) \cdot t&= \cloze{t\cdot t+ t\cdot 3t}\\ &=\cloze{t²+3t²}\\ &=\cloze{4t^2} \end{aligned}
j)   (4aww)k=k4awkw=4akwkw\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} j)\ \ \ (4aw-w)\cdot k &= \cloze{k\cdot 4aw - k\cdot w}\\ &=\cloze{4akw-kw} \end{aligned}