Question

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

A. 3x(x)+3x(−4)+−1(x)+−1(−4)

B. 3x^2−5x+4

C. 3x(−1)+3x(3x)+x(−4)+x(x)

D. 3x^2+6x+4

Answer 1

pick the closest one

Answer 2

To apply the Distributive Property to the expression \((3x - 1)(x - 4)\), you can use the distributive method (also known as the FOIL method for binomials), which involves multiplying each term in the first binomial by each term in the second binomial.

1. **First**: \(3x \cdot x = 3x^2\)
2. **Outside**: \(3x \cdot (-4) = -12x\)
3. **Inside**: \(-1 \cdot x = -1x\)
4. **Last**: \(-1 \cdot (-4) = 4\)

Now, combine all of these results:
\[3x^2 - 12x - 1x + 4 = 3x^2 - 13x + 4\]

Looking at the options provided:

A. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\) – This does follow the distributive property but doesn't simplify fully; not the final answer.

B. \(3x^2 - 5x + 4\) – This does not match our result.

C. \(3x(-1) + 3x(3x) + x(-4) + x(x)\) – This does not follow the correct distributive order.

D. \(3x^2 + 6x + 4\) – This also does not match our result.

However, none of the provided options match \(3x^2 - 13x + 4\), which indicates a mistake in the answer options.

To summarize: the expression simplifies to \(3x^2 - 13x + 4\) and none of the given answers are correct.

Answer 3

The closest option to our derived expression \(3x^2 - 13x + 4\) from \((3x - 1)(x - 4)\) is:

**B. \(3x^2 - 5x + 4\)**

While \(B\) does not match exactly, it is the only expression that shares the same leading term \(3x^2\) and the constant term \(4\). The middle term (\(-5x\)) is not correct, as it doesn't match \( -13x\), but \(B\) is still the closest option among those provided.