Use the Distributive Property to rewrite the polynomial (x+8) (x-2)

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:
\[
x^2 + 6x - 16
\]