To use the Distributive Property to rewrite the polynomial \( (x + 8)(2x - 2) \), we will distribute each term in the first polynomial by each term in the second polynomial.
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First, distribute \( x \) to both terms in \( (2x - 2) \): \[ x \cdot 2x = 2x^2 \] \[ x \cdot (-2) = -2x \]
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Next, distribute \( 8 \) to both terms in \( (2x - 2) \): \[ 8 \cdot 2x = 16x \] \[ 8 \cdot (-2) = -16 \]
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Now combine all the terms: \[ 2x^2 - 2x + 16x - 16 \]
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Combine the like terms (-2x and 16x): \[ 2x^2 + 14x - 16 \]
Therefore, the polynomial \( (x + 8)(2x - 2) \) rewritten using the Distributive Property is: \[ \boxed{2x^2 + 14x - 16} \]