
\ANG{
\textbf{Terme zielgerichtet umformen, insbesondere Summen faktorisieren}

Ergänze und gib die Art des Terms vor sowie nach der Äquivalenzumformung
an.

\begin{tabular}{lllll}
\noalign{\vskip0.5cm}
a) &  & $xy^{3}+y^{2}+\left(xy\right)^{3}$ & $=\:$ & $y^{2}\cdot\left(................................\right)$\tabularnewline[\doublerulesep]
\noalign{\vskip0.5cm}
 & Termart:  & ............................. &  & ...............................\tabularnewline[\doublerulesep]
\noalign{\vskip0.5cm}
b) &  & $\left(\frac{1}{3}a-b\right)\cdot\left(............\right)$ & $=$ & $\frac{1}{4}a^{2}-\frac{3}{4}ab$\tabularnewline[\doublerulesep]
\noalign{\vskip0.5cm}
 & Termart: & ............................. &  & .............................\tabularnewline[\doublerulesep]
\noalign{\vskip0.5cm}
c) &  & $2x$$^{2}y\cdot4xy^{2}$ & $=$ & $2xy\cdot\left(..................\right)$\tabularnewline[\doublerulesep]
\noalign{\vskip\doublerulesep}
 & Termart: & ............................. &  & \tabularnewline[\doublerulesep]
\noalign{\vskip0.5cm}
d) &  & $2x$$^{2}y-4xy^{2}$ & $=$ & $2xy\cdot\left(..................\right)$\tabularnewline[\doublerulesep]
\noalign{\vskip0.5cm}
 & Termart: & ............................. &  & .............................\tabularnewline[\doublerulesep]
\end{tabular}

}
\LSG{Die Terme vor und nach der Äquivalenzumformung lauten:

\begin{tabular}{lllll}
a) &  & $xy^{3}+y^{2}+\left(xy\right)^{3}=y^{2}\cdot\left(xy+1+x^{3}y\right)\qquad$ & linker Term: Summe  & rechter Term: Produkt\tabularnewline[\doublerulesep]
b) &  & $\left(\frac{1}{3}a-b\right)\cdot\left(\frac{3}{4}a\right)=\frac{1}{4}a^{2}-\frac{3}{4}ab$ & linker Term: Produkt & rechter Term: Differenz\tabularnewline[\doublerulesep]
c) &  & $2x$$^{2}y\cdot4xy^{2}$$=2xy\cdot\left(4x^{2}y^{2}\right)$ & linker Term: Produkt & rechter Term: Produkt\tabularnewline[\doublerulesep]
d) &  & $2x$$^{2}y-4xy^{2}$$=2xy\cdot\left(x-y\right)$ & linker Term: Differenz$ $ & rechter Term: Produkt\tabularnewline[\doublerulesep]
\end{tabular}}
