To use the Distributive Property to rewrite the polynomial \((x + 8)(x - 2)\), we can expand it as follows:
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Distribute \(x\) from the first term to both terms in the second polynomial: \[ x \cdot x + x \cdot (-2) = x^2 - 2x \]
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Distribute \(8\) from the first term to both terms in the second polynomial: \[ 8 \cdot x + 8 \cdot (-2) = 8x - 16 \]
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Now, combine all the terms: \[ x^2 - 2x + 8x - 16 = x^2 + 6x - 16 \]
So, the final polynomial is: \[ x^2 + 6x - 16 \]
Filling in the blanks, we have:
- First blank (for \(x^2\)): 1
- Second blank (for \(x\)): 6
- Third blank (for the constant): -16
So the complete answer is: \(x^2 + 6x - 16\).
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