Asked by lit
According to the distributive property , which is a way to rewrite the algebraic expression?(3x-1)(x-4)
A. 3x^2-5x+4
B. 3x(-1)+3x(3x)=x(-4)=x(x)
C. 3x^2+6x+4
D. 3x(x)+3x(-4)+-1(x)+-1(-4)
A. 3x^2-5x+4
B. 3x(-1)+3x(3x)=x(-4)=x(x)
C. 3x^2+6x+4
D. 3x(x)+3x(-4)+-1(x)+-1(-4)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To rewrite the expression \((3x - 1)(x - 4)\) using the distributive property, we can follow these steps:
1. Distribute \(3x\) to both terms in the second parenthesis:
\[
3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x
\]
2. Next, distribute \(-1\) to both terms in the second parenthesis:
\[
-1 \cdot x + (-1) \cdot (-4) = -x + 4
\]
3. Now, combine all these results:
\[
3x^2 - 12x - x + 4 = 3x^2 - 13x + 4
\]
None of the provided answer choices result in the perfectly simplified version of the expression, but it appears that option D (which describes the distribution process) is the most closely related to the distributive property approach.
Thus, the answer is:
**D. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)**
1. Distribute \(3x\) to both terms in the second parenthesis:
\[
3x \cdot x + 3x \cdot (-4) = 3x^2 - 12x
\]
2. Next, distribute \(-1\) to both terms in the second parenthesis:
\[
-1 \cdot x + (-1) \cdot (-4) = -x + 4
\]
3. Now, combine all these results:
\[
3x^2 - 12x - x + 4 = 3x^2 - 13x + 4
\]
None of the provided answer choices result in the perfectly simplified version of the expression, but it appears that option D (which describes the distribution process) is the most closely related to the distributive property approach.
Thus, the answer is:
**D. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)**
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