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To use the Distributive Property (also known as the FOIL method for binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we will multiply each term in the first binomial by each term in the second binomial.
1. First, multiply the first terms:
\(x \cdot x = x^2\)
2. Next, multiply the outer terms:
\(x \cdot (-2) = -2x\)
3. Then, multiply the inner terms:
\(8 \cdot x = 8x\)
4. Finally, multiply the last terms:
\(8 \cdot (-2) = -16\)
Now, we combine all these results together:
\[
x^2 - 2x + 8x - 16
\]
Now, combine the like terms \(-2x + 8x\):
\[
x^2 + 6x - 16
\]
So, in the form \(x^2 + __x + __\), we have:
\[
\text{First blank: } 6, \quad \text{Second blank: } -16
\]
Thus, our final answer is:
\[
x^2 + 6x - 16
\]