To complete the area model based on the given expression, let’s first understand the layout and fill in the blanks based on the multiplication of polynomials.
We have an area model with:
- The rows corresponding to the polynomial terms \( -4x^{11} \)
- The columns corresponding to the polynomial terms \( 3x^{-3}, -2x^{-5}, -4 \)
The multiplication based on area can be given by distributing the first term across all terms below it.
Given this structure, the missing entries in the model will be the products of the terms from the rows and the columns.
Filling in the model:
-
First column:
- \(-4x^{11} \times 3x^{-3} = -12x^{8}\)
-
Second column:
- \(-4x^{11} \times -2x^{-5} = 8x^{6}\)
-
Third column:
- \(-4x^{11} \times -4 = 16x^{11}\)
Your completed area model will look like this:
\[ \begin{array}{c|c|c|c} & 3x^{-3} & -2x^{-5} & -4 \ \hline -4x^{11} & -12x^{8} & 8x^{6} & 16x^{11} \ \end{array} \]
So, the final answers for the blanks are:
- The first blank: \(-12x^{8}\)
- The second blank: \(8x^{6}\)
- The third blank: \(16x^{11}\)