To apply the Distributive Property to the expression \((3x−1)(x−4)\), we need to distribute each term in the first parenthesis with every term in the second parenthesis.
Let's break it down step by step:
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Distribute \(3x\) to both \(x\) and \(-4\): \[ 3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x \]
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Distribute \(-1\) to both \(x\) and \(-4\): \[ -1 \cdot x + (-1) \cdot (-4) = -x + 4 \]
Now combine all the terms together: \[ 3x^2 - 12x - x + 4 \] Combine the like terms (-12x and -x): \[ 3x^2 - 13x + 4 \]
Thus, the expression can be rewritten in a simplified form. However, none of your provided options accurately represent the result of the multiplication of the expression.
The correct final answer is: \[ 3x^2 - 13x + 4 \]
If we were to compare with the provided options, the closest term would seem to be "3x^2 - 5x + 4," but keep in mind that this expression is incorrect based on the accurate application of the distributive property.
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