Question

According to the Distributive Property, which is a way to rewrite the algebraic expression (3x−1)(x−4) ?(1 point) Responses 3x2+6x+4 3 x squared plus 6 x plus 4 3x2−5x+4 3 x squared minus 5 x plus 4 3x(x)+3x(−4)+−1(x)+−1(−4) 3 x left parenthesis x right parenthesis plus 3 x left parenthesis negative 4 right parenthesis plus negative 1 left parenthesis x right parenthesis plus negative 1 left parenthesis negative 4 right parenthesis 3x(−1)+3x(3x)+x(−4)+x(x)

Answer 1

To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the Distributive Property, we can use the distributive method (also known as FOIL for binomials), which involves multiplying each term in the first parenthesis by each term in the second parenthesis.

Let's go through the multiplication step-by-step:

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: \(-1 \cdot x = -x\)
4. **Last:** Multiply the last terms: \(-1 \cdot (-4) = 4\)

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

Combine the like terms for the \(x\) terms:
- \(-12x - x = -13x\)

Thus, the expression becomes:
- \(3x^2 - 13x + 4\)

None of the options you presented match the resulting expression precisely. However, based on the options, it looks like there may have been some misunderstanding in either the transcription or the choices given. The correct expression from the operation is **3x² - 13x + 4**. Please check the original options again for a potential match or error!