Question

According to the distributive property, which is a way to rewrite the algebraic expression (3x-1)(x-4)?
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)

Answer 1

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:

1. Distribute \(3x\) to both \(x\) and \(-4\).
2. 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. \(3x(x)+3x(-4)+-1(x)+-1(-4)\)**