Question

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

Answer 1

To rewrite the expression \((3x - 1)(x - 4)\) using the distributive property, you need to distribute each term in the first parenthesis by each term in the second parenthesis.

Here's how you can do it step by step:

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

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

3. Now, combine all the terms together:
\[
3x^2 - 12x - x + 4
\]

4. Combine like terms \(-12x\) and \(-x\):
\[
3x^2 - 13x + 4
\]

So, the expression \((3x - 1)(x - 4)\) can be rewritten as:
\[
3x^2 - 13x + 4
\]