To rewrite the algebraic expression \((3x-1)(x-4)\) using the distributive property (also known as the FOIL method for binomials), we can apply the distributive property as follows:
- Distribute \(3x\) to both \(x\) and \(-4\).
- Distribute \(-1\) to both \(x\) and \(-4\).
Here's the calculation step by step:
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)
Now we can combine all these results together:
\[ 3x^2 - 12x - x + 4 \]
Combine the like terms \(-12x\) and \(-x\):
\[ 3x^2 - 13x + 4 \]
None of the options presented exactly match the expression we calculated. However, if we need to check the options provided:
A. \(3x²+6x+4\)
B. \(3x²-5x+4\)
C. \(3x(x)+3x(-4)+-1(x)+-1(-4)\)
D. \(3x(-1)+3x(3x)+x(-4)+x(x)\)
Among these options, C shows the breakdown using the distributive property correctly.
Therefore, the best choice for rewriting \((3x-1)(x-4)\) according to the distributive property is:
C. \(3x(x)+3x(-4)+-1(x)+-1(-4)\)