To use the Distributive Property to rewrite the polynomial \((x + 8)(x - 2)\), we'll distribute each term in the first parenthesis to each term in the second parenthesis.
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Distribute \(x\): \[ x \cdot x + x \cdot (-2) = x^2 - 2x \]
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Distribute \(8\): \[ 8 \cdot x + 8 \cdot (-2) = 8x - 16 \]
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Now, combine all the terms: \[ x^2 - 2x + 8x - 16 \] Combine the like terms \(-2x\) and \(8x\): \[ x^2 + 6x - 16 \]
So, the polynomial \((x + 8)(x - 2)\) can be rewritten as: \[ \boxed{x^2 + 6x - 16} \] where \(1\) is the coefficient of \(x^2\), \(6\) is the coefficient of \(x\), and \(-16\) is the constant term.