Question

According to the Distributive Property, which is a way to rewrite the algebraic expression (3x−1)(x−4) ?(1 point)
Responses

Answer 1

To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the Distributive Property, you will distribute each term in the first parentheses to each term in the second parentheses. Here's how it's done step by step:

1. Distribute \(3x\) to both terms in \((x - 4)\):
- \(3x \cdot x = 3x^2\)
- \(3x \cdot (-4) = -12x\)

2. Distribute \(-1\) to both terms in \((x - 4)\):
- \(-1 \cdot x = -1x\)
- \(-1 \cdot (-4) = 4\)

Now combine all the results:

\[
3x^2 - 12x - 1x + 4
\]

Combine the like terms \(-12x - 1x\):

\[
3x^2 - 13x + 4
\]

So, the expression \((3x - 1)(x - 4)\) can be rewritten as:

\[
\boxed{3x^2 - 13x + 4}
\]