To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the Distributive Property, you need to distribute each term in the first parentheses by each term in the second parentheses. Here’s how it works step by step:
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Distribute \(3x\) across \((x - 4)\): \[ 3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x \]
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Distribute \(-1\) across \((x - 4)\): \[ -1 \cdot x + (-1) \cdot (-4) = -x + 4 \]
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Now, combine all the distributed terms: \[ 3x^2 - 12x - x + 4 \]
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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: \[ 3x^2 - 13x + 4 \]