To use the Distributive Property to rewrite the polynomial \( (x+8)(x-2) \), we will distribute each term in the first parenthesis \( (x + 8) \) to each term in the second parenthesis \( (x - 2) \).
Here’s how it works step by step:
1. Distribute \( x \) in \( (x + 8) \):
\[
x \cdot x = x^2
\]
\[
x \cdot (-2) = -2x
\]
2. Distribute \( 8 \) in \( (x + 8) \):
\[
8 \cdot x = 8x
\]
\[
8 \cdot (-2) = -16
\]
3. Now, combine all the results:
\[
x^2 - 2x + 8x - 16
\]
4. Combine the like terms \(-2x\) and \(8x\):
\[
x^2 + 6x - 16
\]
Thus, the polynomial \( (x+8)(x-2) \) can be rewritten as:
\[
x^2 + 6x - 16
\]