To fill in the area model for the expression \( 8(6z + 5) \), you can break it down as follows:
- The area model divides \( 8(6z + 5) \) into two parts: one for \( 6z \) and one for \( 5 \).
- Each section will be multiplied by \( 8 \).
The area model looks like this:
\[ \begin{array}{|c|c|c|} \hline & 6z & +5 \ \hline 8 & 48z & 40 \ \hline \end{array} \]
Now, let's fill in the missing values:
- In the cell where \( 8 \) intersects with \( 6z \), you calculate \( 8 \times 6z = 48z \).
- In the cell where \( 8 \) intersects with \( 5 \), you calculate \( 8 \times 5 = 40 \).
Putting it all together:
\[ 8(6z + 5) = 48z + 40 \]
So, according to the area model, \( 8(6z + 5) = 48z + 40 \).
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