To find the product of \( 5(3n - 3) \) using an area model, we can break down the expression into manageable parts.
First, we need to factor or distribute the expression \( 3n - 3 \):
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Factor out the common term:
\( 3n - 3 = 3(n - 1) \) -
Rewrite the expression:
Now we can rewrite the original expression as:
\[ 5(3(n - 1)) = (5 \cdot 3)(n - 1) = 15(n - 1) \]
Area Model Representation
You can visualize this using an area model as follows:
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Create a rectangle split into two parts: one for \( 5 \cdot 3n \) and another for \( 5 \cdot (-3) \).
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Break down the calculations:
Breakdown of Area Model:
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First rectangle (for \( 3n \) part):
One side will be \( 5 \) and the other will be \( 3n \), giving you an area of \( 15n \). -
Second rectangle (for \( -3 \) part):
One side will still be \( 5 \) and the other side will be \( -3 \), giving you an area of \( -15 \).
Area Model Summary
The area model can be represented as:
\[ \begin{array}{|c|c|} \hline 5 & -15 \ \hline 15n & -15 \ \hline \end{array} \]
Final Result
The final result when combining the areas is:
\[ 15n - 15 \] So, \( 5(3n - 3) = 15n - 15 \).
This is the complete simplified form of the expression using an area model to organize the terms.