To rewrite the polynomial \((x + 8)(x - 2)\) using the distributive property, we will distribute each term in the first parentheses by each term in the second parentheses.
-
Distribute \(x\) across \((x - 2)\): \[ x \cdot x + x \cdot (-2) = x^2 - 2x \]
-
Distribute \(8\) across \((x - 2)\): \[ 8 \cdot x + 8 \cdot (-2) = 8x - 16 \]
Now, combine all the terms: \[ x^2 - 2x + 8x - 16 \]
Combine the like terms \(-2x\) and \(8x\): \[ x^2 + 6x - 16 \]
Thus, the rewritten polynomial is: \[ x^2 + 6x - 16 \]