To rewrite the polynomial \((x+8)(x-2)\) using the distributive property, you can distribute each term in the first parentheses to each term in the second parentheses.
Here's how it works step by step:
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Distribute \(x\) in \((x + 8)\) to both terms in \((x - 2)\): \[ x \cdot x + x \cdot (-2) = x^2 - 2x \]
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Distribute \(8\) in \((x + 8)\) to both terms in \((x - 2)\): \[ 8 \cdot x + 8 \cdot (-2) = 8x - 16 \]
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Now, combine all the terms from both distributions: \[ x^2 - 2x + 8x - 16 \]
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Combine like terms: \[ x^2 + (8x - 2x) - 16 = x^2 + 6x - 16 \]
So, the polynomial \((x + 8)(x - 2)\) can be rewritten as: \[ x^2 + 6x - 16 \]
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