To rewrite the polynomial \((x + 8)(2x - 2)\) using the Distributive Property, you need to distribute each term in the first polynomial \( (x + 8) \) to each term in the second polynomial \( (2x - 2) \).
Here are the steps:
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Distribute \(x\) to both terms in \( (2x - 2) \): \[ x \cdot 2x = 2x^2 \] \[ x \cdot (-2) = -2x \]
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Now distribute \(8\) to both terms in \( (2x - 2) \): \[ 8 \cdot 2x = 16x \] \[ 8 \cdot (-2) = -16 \]
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Now combine all the results: \[ 2x^2 - 2x + 16x - 16 \]
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Combine like terms: \[ 2x^2 + ( -2x + 16x ) - 16 = 2x^2 + 14x - 16 \]
So, the polynomial \((x + 8)(2x - 2)\) can be rewritten as: \[ \boxed{2x^2 + 14x - 16} \]