To rewrite the algebraic expression \((3x-1)(x-4)\) using the Distributive Property, let's apply the FOIL method (First, Outside, Inside, Last):
1. **First:** Multiply the first terms: \(3x \cdot x = 3x^2\)
2. **Outside:** Multiply the outer terms: \(3x \cdot (-4) = -12x\)
3. **Inside:** Multiply the inner terms: \(-1 \cdot x = -1x\)
4. **Last:** Multiply the last terms: \(-1 \cdot (-4) = 4\)
Next, combine all the results:
\[
3x^2 - 12x - 1x + 4 = 3x^2 - 13x + 4
\]
Now, let's evaluate the provided options:
A. \(3x^2 - 5x + 4\) (Incorrect)
B. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\) (This is the correct expansion form)
C. \(3x^2 + 6x + 4\) (Incorrect)
D. \(3x(-1) + 3x(3x) + x(-4) + x(x)\) (Incorrect)
Thus, the correct way to rewrite the expression using the Distributive Property from the choices given is:
**B.** \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)