Use the commutative and associative properties to reorder the expression and group like-terms together.

\(\displaystyle 6t \cdot 7t = 6\cdot 7\cdot t \cdot t = 42 \cdot t^{2}=42t^2\)

\(\displaystyle a \bigstar b = ab-a\), so

\(\displaystyle N \bigstar (-N) = N (-N ) - N= -N^{2} - N\)

\(\displaystyle (-N) \bigstar N = (-N )N - (-N)= -N^{2}+N\)

Since \(\displaystyle N\) is positive, 

\(\displaystyle N > -N\), 

and by the addition property of inequality,

\(\displaystyle -N^{2}+N > -N^{2} - N\)

and 

\(\displaystyle (-N) \bigstar N > N \bigstar (-N)\)

We demonstrate that all four of the expressions are equivalent to \(\displaystyle 20y\).

By the associative property of multiplication,

\(\displaystyle 4 (5y) = (4 \cdot 5) \cdot y = 20y\)

and

\(\displaystyle 5 (4y) = (5\cdot 4) \cdot y = 20y\)

By combining like terms, and applying the distribution property:

\(\displaystyle 5(3y + y) = 5(3y + 1 y) = 5[ (3 + 1 ) y] = 5 \left ( 4 y \right )= 20y\)

\(\displaystyle 4 (3y + 2y) = 4\left [ (3 + 2) y \right ] = 4\left ( 5y\right ) = 20y\)

To solve this problem, we multiply \(\displaystyle 1\) by the ones position and the tens position. 

\(\displaystyle 1\times0=0\)

\(\displaystyle 1\times1=1\)

\(\displaystyle \frac{\begin{array}[b]{r}10\\ \times\ 1\end{array}}{ \ \ \space10}\)

To solve this problem, we multiply \(\displaystyle 2\) by the ones position and the tens position. 

\(\displaystyle 2\times0=0\)

\(\displaystyle 2\times2=4\)

\(\displaystyle \frac{\begin{array}[b]{r}20\\ \times\ 2\end{array}}{ \ \ \space40}\)

To solve this problem, we multiply \(\displaystyle 4\) by the ones position and the tens position. 

\(\displaystyle 4\times0=0\)

\(\displaystyle 4\times4=16\)

\(\displaystyle \frac{\begin{array}[b]{r}40\\ \times\ 4\end{array}}{ \ \space160}\)

To solve this problem, we multiply \(\displaystyle 5\) by the ones position and the tens position. 

\(\displaystyle 5\times0=0\)

\(\displaystyle 5\times5=25\)

\(\displaystyle \frac{\begin{array}[b]{r}50\\ \times\ 5\end{array}}{ \ \space250}\)

To solve this problem, we multiply \(\displaystyle 6\) by the ones position and the tens position. 

\(\displaystyle 6\times0=0\)

\(\displaystyle 6\times6=36\)

\(\displaystyle \frac{\begin{array}[b]{r}60\\ \times\ 6\end{array}}{ \ \space360}\)

To solve this problem, we multiply \(\displaystyle 7\) by the ones position and the tens position. 

\(\displaystyle 7\times0=0\)

\(\displaystyle 7\times7=49\)

\(\displaystyle \frac{\begin{array}[b]{r}70\\ \times\ 7\end{array}}{ \ \space490}\)

To solve this problem, we multiply \(\displaystyle 8\) by the ones position and the tens position. 

\(\displaystyle 8\times0=0\)

\(\displaystyle 8\times8=64\)

\(\displaystyle \frac{\begin{array}[b]{r}80\\ \times\ 8\end{array}}{ \ \space640}\)