To rewrite the expression \((3x - 1)(x - 4)\) using the distributive property, you need to distribute each term in the first parenthesis by each term in the second parenthesis.
Here's how you can do it step by step:
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Distribute \(3x\) to both terms in \((x - 4)\): \[ 3x \cdot x - 3x \cdot 4 = 3x^2 - 12x \]
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Distribute \(-1\) to both terms in \((x - 4)\): \[ -1 \cdot x + (-1) \cdot (-4) = -x + 4 \]
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Now, combine all the terms together: \[ 3x^2 - 12x - x + 4 \]
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Combine like terms \(-12x\) and \(-x\): \[ 3x^2 - 13x + 4 \]
So, the expression \((3x - 1)(x - 4)\) can be rewritten as: \[ 3x^2 - 13x + 4 \]