The Distributive Property states that \( a(b + c) = ab + ac \). To use this property to rewrite the expression \((3x - 1)(x - 4)\), you will distribute each term in the first parenthesis by each term in the second parenthesis.
Here’s how it works 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 these results together: \[ 3x^2 - 12x - x + 4 \]
Combine like terms (\(-12x\) and \(-x\)): \[ 3x^2 - 13x + 4 \]
Thus, the expression \((3x - 1)(x - 4)\) can be rewritten using the Distributive Property as: \[ 3x^2 - 13x + 4 \]