To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the Distributive Property, you will need to distribute each term in the first parentheses by each term in the second parentheses.
Here’s how it’s done 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 \(-4\): \[ -1 \cdot x + (-1) \cdot (-4) = -x + 4 \]
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Now, combine all the terms: \[ 3x^2 - 12x - x + 4 \]
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Combine like terms \(-12x\) and \(-x\): \[ -12x - x = -13x \]
Therefore, the expression \((3x - 1)(x - 4)\) can be rewritten as: \[ 3x^2 - 13x + 4 \]
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