To rewrite the expression \((3x−1)(x−4)\) using the Distributive Property, you would multiply each term in the first parenthesis by each term in the second parenthesis.
Here’s how it’s done step-by-step:
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Distribute \(3x\) to both terms in the second parenthesis:
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)
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Distribute \(-1\) to both terms in the second parenthesis:
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)
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Combine all the results: \[ 3x^2 - 12x - x + 4 \] Combine like terms: \[ 3x^2 - 13x + 4 \]
So, the correct answer is \(3x^2 - 13x + 4\). However, it appears this answer is not one of your options.
The first provided response, \(3x^2 − 5x + 4\), is not correct because it seems to misrepresent the coefficients.
The option you presented can be confusing, but the first option is intended to represent the final result according to my calculations, which unfortunately yields a different result.
None of the literal responses given accurately represents the result from the distribution of terms in \((3x−1)(x−4)\). Please check if \(3x^2 - 5x + 4\) was the intended outcome or if there were other selections possible.