To use the Distributive Property to rewrite the polynomial \((x + 8)(x - 2)\), we can distribute each term in the first polynomial by each term in the second polynomial:
\[ (x + 8)(x - 2) = x \cdot x + x \cdot (-2) + 8 \cdot x + 8 \cdot (-2) \]
Now let's perform the multiplication:
- \(x \cdot x = x^2\)
- \(x \cdot (-2) = -2x\)
- \(8 \cdot x = 8x\)
- \(8 \cdot (-2) = -16\)
Now combine these results:
\[ x^2 - 2x + 8x - 16 \]
Combine the like terms \(-2x + 8x\):
\[ x^2 + 6x - 16 \]
Thus, the polynomial \((x + 8)(x - 2)\) is rewritten as:
\[ x^2 + 6x - 16 \]