To rewrite the expression \((3x - 1)(x - 4)\) using the Distributive Property, we need to distribute each term in the first parentheses to each term in the second parentheses.
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Distributing \(3x\):
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)
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Distributing \(-1\):
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)
Now combine all the terms: \[ 3x^2 - 12x - x + 4 \] Combine like terms: \[ 3x^2 - 13x + 4 \]
None of the provided responses seem to match this directly. However, let’s check each option:
- 3x² + 6x + 4 (Not correct)
- 3x² - 5x + 4 (Not correct)
- 3x(x) + 3x(-4) + -1(x) + -1(-4) (This expands correctly to our earlier steps but isn't simplified)
- 3x(-1) + 3x(3x) + x(-4) + x(x) (Not correct; has wrong terms)
The expression that best represents \((3x - 1)(x - 4)\) using the Distributive Property, in a general simplified form, is: \[ \boxed{3x^2 - 13x + 4} \]
However, since that isn't an option, the closest option to the expansion steps is the third one, even though it needs simplification: 3x(x) + 3x(−4) + −1(x) + −1(−4)