• Ausmultiplizieren (2)
  • 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(5x+6)=15x+18\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} a)\ \ \ 3(5x+6) &=\cloze{15x+18} \end{aligned}
b)   3(8y+5)=24y+15\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} b)\ \ \ 3(8y+5) &=\cloze{24y+15} \end{aligned}
c)   5(56y)=2530y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} c)\ \ \ 5(5-6y) &=\cloze{25-30y} \end{aligned}
d)   6(97x)=5442x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} d)\ \ \ 6(9-7x) &=\cloze{54-42x} \end{aligned}
e)   2(3x+4y)=6x8y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} e)\ \ \ 2(3x+4y) &=\cloze{6x-8y} \end{aligned}
f)   7(5y6z)=35y42z\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} f)\ \ \ 7(5y-6z) &=\cloze{35y-42z} \end{aligned}
g)   9(8x2z)=72x18z\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} g)\ \ \ 9(8x-2z) &=\cloze{72x-18z} \end{aligned}
h)   8(7z+9y)=56z+72y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} h)\ \ \ 8(7z+9y) &=\cloze{56z+72y} \end{aligned}
i)   (4a2b)5=20a10b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} i)\ \ \ (4a-2b)5 &=\cloze{20a-10b} \end{aligned}
j)   (7z+9y)3=21z+18y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} j)\ \ \ (7z+9y)3 &=\cloze{21z+18y} \end{aligned}
k)   (5x+6)4=20x+24\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} k)\ \ \ (5x+6)4 &=\cloze{20x+24} \end{aligned}
l)   (8y+5)2=16y+10\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} l)\ \ \ (8y+5)2 &=\cloze{16y+10} \end{aligned}
m)   (56y)8=4048y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} m)\ \ \ (5-6y)8 &=\cloze{40-48y} \end{aligned}
n)   (97x)3=2721x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} n)\ \ \ (9-7x)3 &=\cloze{27-21x} \end{aligned}
o)   (3x+4y)10=30x40y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} o)\ \ \ (3x+4y)10 &=\cloze{30x-40y} \end{aligned}
p)   (5y6z)3=15y18z\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} p)\ \ \ (5y-6z)3 &=\cloze{15y-18z} \end{aligned}
q)   (8x2z)4=32x8z\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} q)\ \ \ (8x-2z)4 &=\cloze{32x-8z} \end{aligned}
r)   (7z+9y)5=35z+45y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} r)\ \ \ (7z+9y)5 &=\cloze{35z+45y} \end{aligned}
s)   4(2x+2y)=8x+8y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} s)\ \ \ 4(2x+2y) &=\cloze{8x+8y} \end{aligned}
t)   9(8b+5a)=72b+45a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} t)\ \ \ 9(8b+5a) &=\cloze{72b+45a} \end{aligned}
u)   (4x9y)5=20x45y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} u)\ \ \ (4x-9y)5 &=\cloze{20x-45y} \end{aligned}
v)   (3a+9b)8=24a+72b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} v)\ \ \ (3a+9b)8 &=\cloze{24a+72b} \end{aligned}
w)   3(3x+6y)=9x+18y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} w)\ \ \ 3(3x+6y) &=\cloze{9x+18y} \end{aligned}
x)   3(2e+6a)=6e+18a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} x)\ \ \ 3(2e+6a) &=\cloze{6e+18a} \end{aligned}
y)   (4p2q)4=16p8q\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} y)\ \ \ (4p-2q)4 &=\cloze{16p-8q} \end{aligned}
z)   (4z+2y)6=24z+12y\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{526060}{\large{$\displaystyle #1$}}}}}} \begin{aligned} z)\ \ \ (4z+2y)6 &=\cloze{24z+12y} \end{aligned}