To rewrite the algebraic expression \((3x-1)(x-4)\) using the Distributive Property, we can distribute each term in the first parentheses by each term in the second parentheses.
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 the terms: \[ 3x^2 - 12x - x + 4 \] Combining like terms: \[ 3x^2 - 13x + 4 \]
None of the provided answer options match exactly, but evaluating the options given:
- A. \(3x(-1)+3x(3x)+x(-4)+x(x)\) → This does not represent the expression correctly.
- B. \(3x^2 - 5x + 4\) → Incorrect because the middle term doesn't match.
- C. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\) → This represents the correct process of distributing.
- D. \(3x^2 + 6x + 4\) → Incorrect because the terms do not match.
Based on this analysis, the best answer would be C, as it reflects the correct distribution process. However, it does not directly reduce to the final expression, which is \(3x^2 - 13x + 4\).
1 answer