To use the Distributive Property to rewrite the expression \((3x - 1)(x - 4)\), we can distribute each term in the first parenthesis to each term in the second parenthesis:
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Multiply \(3x\) by both terms in \((x - 4)\):
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)
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Multiply \(-1\) by both terms in \((x - 4)\):
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)
Now, combine all the terms: \[ 3x^2 - 12x - x + 4 \]
Combine the like terms (\(-12x - x\)): \[ 3x^2 - 13x + 4 \]
So, the correct rewritten expression using the Distributive Property is: \[ 3x^2 - 13x + 4 \]
However, based on the provided response options, it seems that the expression you listed as the answer was "3x^2 - 5x + 4," which is incorrect based on the calculations shown above. The correct response is not listed among the options you've provided.
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