To use the distributive property to rewrite the expression \((x + 4)(x - 6)\), we can distribute each term in the first polynomial to each term in the second polynomial.
Here's how it works step by step:
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Distribute \(x\) to both terms in \((x - 6)\): \[ x \cdot x + x \cdot (-6) = x^2 - 6x \]
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Distribute \(4\) to both terms in \((x - 6)\): \[ 4 \cdot x + 4 \cdot (-6) = 4x - 24 \]
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Now, combine all the terms: \[ x^2 - 6x + 4x - 24 \]
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Combine like terms: \[ x^2 - 2x - 24 \]
So, the result of rewriting the polynomial \((x + 4)(x - 6)\) using the distributive property is: \[ \boxed{x^2 - 2x - 24} \]
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