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 \( a(b + c) = ab + ac \). In the case of the expression \( (3x - 1)(x - 4) \), we can apply the distributive property (also known as the FOIL method for binomials) to rewrite it.

Let's distribute each term in the first binomial \( (3x - 1) \) to each term in the second binomial \( (x - 4) \):

1. **First:** Multiply the first terms: \( 3x \cdot x = 3x^2 \)
2. **Outer:** Multiply the outer terms: \( 3x \cdot (-4) = -12x \)
3. **Inner:** Multiply the inner terms: \( -1 \cdot x = -1x \)
4. **Last:** Multiply the last terms: \( -1 \cdot (-4) = 4 \)

Now, combine all these results together:

\[
3x^2 - 12x - 1x + 4
\]

Combine like terms (the \( -12x \) and \( -1x \)):

\[
3x^2 - 13x + 4
\]

Thus, the expression \( (3x - 1)(x - 4) \) can be rewritten as:

\[
\boxed{3x^2 - 13x + 4}
\]