Question

rewrite (3x-1)*(x-4) with the distributive property

Answer 1

To rewrite \((3x - 1)(x - 4)\) using the distributive property, we apply the distributive law, which involves multiplying each term in the first parentheses by each term in the second parentheses.

Here’s the step-by-step breakdown:

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

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

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

4. Finally, combine like terms:
\[
3x^2 - 13x + 4
\]

So, the expression \((3x - 1)(x - 4)\) rewritten using the distributive property is:
\[
3x^2 - 13x + 4
\]