Question

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

Answer 1

The Distributive Property states that \( a(b + c) = ab + ac \). To apply this property to the expression \( (3x - 1)(x - 4) \), we need to distribute each term in the first factor to each term in the second factor.

Let's do this 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 \( (x - 4) \):
- \( -1 \cdot x = -x \)
- \( -1 \cdot (-4) = 4 \)

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

Next, combine the like terms \( -12x \) and \( -x \):
\[
3x^2 - 13x + 4
\]

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