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 will need to distribute each term in the first parentheses by each term in the second parentheses.

Here’s how it’s done step by step:

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

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

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

4. Combine like terms \(-12x\) and \(-x\):
\[
-12x - x = -13x
\]

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