To use the Distributive Property to rewrite the polynomial \((x + 8)(2x - 2)\), we will distribute each term in the first polynomial to each term in the second polynomial.
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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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Distribute \(8\) to both terms in \(2x - 2\): \[ 8 \cdot 2x = 16x \] \[ 8 \cdot (-2) = -16 \]
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Now combine all the distributed terms: \[ 2x^2 - 2x + 16x - 16 \]
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Combine the like terms \(-2x\) and \(16x\): \[ 2x^2 + 14x - 16 \]
So, the rewritten polynomial is: \[ []x^2 + []x + [_] \]
Where:
- The coefficient of \(x^2\) is \(2\)
- The coefficient of \(x\) is \(14\)
- The constant term is \(-16\)
Thus, the final answer is: \[ 2x^2 + 14x - 16 \]
So, in the blanks:
- \(2\)
- \(14\)
- \(-16\)