The Distributive Property states that \( a(b + c) = ab + ac \). To apply this property to the expression \( (3x - 1)(x - 4) \), we need to distribute each term in the first factor to each term in the second factor.
Let's do this step by step:
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Distribute \( 3x \) to both terms in \( (x - 4) \):
- \( 3x \cdot x = 3x^2 \)
- \( 3x \cdot (-4) = -12x \)
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Distribute \( -1 \) to both terms in \( (x - 4) \):
- \( -1 \cdot x = -x \)
- \( -1 \cdot (-4) = 4 \)
Now, combine all these results together: \[ 3x^2 - 12x - x + 4 \]
Next, combine the like terms \( -12x \) and \( -x \): \[ 3x^2 - 13x + 4 \]
So, the expression \( (3x - 1)(x - 4) \) can be rewritten as: \[ 3x^2 - 13x + 4 \]