To use the Distributive Property to rewrite the polynomial \((x + 8)(x - 2)\), we will distribute each term in the first binomial \((x + 8)\) to each term in the second binomial \((x - 2)\).
Here are the steps:
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Distribute \(x\) to both \(x\) and \(-2\): \[ x \cdot x + x \cdot (-2) = x^2 - 2x \]
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Distribute \(8\) to both \(x\) and \(-2\): \[ 8 \cdot x + 8 \cdot (-2) = 8x - 16 \]
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Combine all the terms from the distributions: \[ x^2 - 2x + 8x - 16 \]
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Combine like terms: \[ x^2 + 6x - 16 \]
Now, we can fill in the boxes:
\[ \text{Box} , x^2 + \text{Box} , 6x + \text{Box} , (-16) \]
So, the final rewritten polynomial is: \[ x^2 + 6x - 16 \]
The filled-in boxes will be:
- Box for \(x^2\): 1 (since it can be written as \(1x^2\))
- Box for \(6x\): 6
- Box for \(-16\): -16