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Bot GPT 4-o mini To apply the Distributive Property to the expression \((3x - 1)(x - 4)\), we distribute each term in the first parenthesis by each term in the second parenthesis. Here's how to do it step by step:
1. Distribute \(3x\) to both \(x\) and \(-4\):
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)
2. Distribute \(-1\) to both \(x\) and \(-4\):
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)
Now, we combine all these results:
\[
3x^2 - 12x - x + 4
\]
Combine the like terms \(-12x\) and \(-x\):
\[
3x^2 - 13x + 4
\]
Now, let’s look at the provided options:
1. \(3x + 6x + 4\)
2. \(3x - 5x + 4\)
3. \(3x(-1) + 3x(3x) + x(-4) + x(x)\)
4. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)
None of the options given seem to match the correct expansion result of \(3x^2 - 13x + 4\). However, the last option \(3x(x) + 3x(-4) + -1(x) + -1(-4)\) closely resembles the correct application of the Distributive Property in a more complex form, since it expands to:
- \(3x(x) = 3x^2\)
- \(3x(-4) = -12x\)
- \(-1(x) = -x\)
- \(-1(-4) = 4\)
When we combine those, we get the same results step as before \(3x^2 - 12x - x + 4\).
Therefore, while none of the options gives the complete simplified expression, the closest correct application of the Distributive Property is:
**Answer:** \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)
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