Question

According to the Distributive Property, which is a way to rewrite the algebraic expression (3x-1)(x-4)

Answer 1

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

1. Distribute \(3x\) across \((x - 4)\):
\[
3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x
\]

2. Distribute \(-1\) across \((x - 4)\):
\[
-1 \cdot x + (-1) \cdot (-4) = -x + 4
\]

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

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

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