Question
Use the distributive property to rewrite the algebraic expression (3x - 1) (x - 4)
3x^2 + 6x + 4
3x(x) + 3x(-4) + -1(x) + -1(-4)
3x(-1) + 3x(3x) + x(-4) + x(x)
3x^2 - 5x + 4
3x^2 + 6x + 4
3x(x) + 3x(-4) + -1(x) + -1(-4)
3x(-1) + 3x(3x) + x(-4) + x(x)
3x^2 - 5x + 4
Answers
Answer
Pick from the answers
Answer
Use the distributive property to rewrite the algebraic expression (3x - 1) (x - 4)
3x^2 + 6x + 4
3x(x) + 3x(-4) + -1(x) + -1(-4)
3x(-1) + 3x(3x) + x(-4) + x(x)
3x^2 - 5x + 4
PICK FROM ONE OF THE FOUR ANSWERS.
3x^2 + 6x + 4
3x(x) + 3x(-4) + -1(x) + -1(-4)
3x(-1) + 3x(3x) + x(-4) + x(x)
3x^2 - 5x + 4
PICK FROM ONE OF THE FOUR ANSWERS.
Answered by
GPT-4o mini
To use the distributive property to rewrite the expression \((3x - 1)(x - 4)\), we'll multiply each term in the first parentheses by each term in the second parentheses.
1. Distribute \(3x\) to each term in \((x - 4)\):
\[
3x \cdot x = 3x^2
\]
\[
3x \cdot (-4) = -12x
\]
2. Distribute \(-1\) to each term in \((x - 4)\):
\[
-1 \cdot x = -x
\]
\[
-1 \cdot (-4) = 4
\]
Now, combine all the terms:
\[
3x^2 - 12x - x + 4
\]
Combine the like terms \(-12x\) and \(-x\):
\[
3x^2 - 13x + 4
\]
So the simplified expression using the distributive property is:
\[
3x^2 - 13x + 4
\]
1. Distribute \(3x\) to each term in \((x - 4)\):
\[
3x \cdot x = 3x^2
\]
\[
3x \cdot (-4) = -12x
\]
2. Distribute \(-1\) to each term in \((x - 4)\):
\[
-1 \cdot x = -x
\]
\[
-1 \cdot (-4) = 4
\]
Now, combine all the terms:
\[
3x^2 - 12x - x + 4
\]
Combine the like terms \(-12x\) and \(-x\):
\[
3x^2 - 13x + 4
\]
So the simplified expression using the distributive property is:
\[
3x^2 - 13x + 4
\]
Answered by
GPT-4o mini
Based on your previous question regarding the expression \((3x - 1)(x - 4)\), the correct answer after applying the distributive property is:
\[
3x^2 - 13x + 4
\]
If you have specific options to choose from, please provide them, and I will help you select the accurate one!
\[
3x^2 - 13x + 4
\]
If you have specific options to choose from, please provide them, and I will help you select the accurate one!
Answered by
GPT-4o mini
Let's review the options provided after using the distributive property on the expression \((3x - 1)(x - 4)\):
The correct expansion using the distributive property gives us:
1. \(3x \cdot x = 3x^2\)
2. \(3x \cdot (-4) = -12x\)
3. \(-1 \cdot x = -x\)
4. \(-1 \cdot (-4) = 4\)
Combining all the terms yields:
\[
3x^2 - 12x - x + 4 = 3x^2 - 13x + 4
\]
Now, looking at the four options you provided:
1. \(3x^2 + 6x + 4\)
2. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)
3. \(3x(-1) + 3x(3x) + x(-4) + x(x)\)
4. \(3x^2 - 5x + 4\)
None of the options match the correct result of \(3x^2 - 13x + 4\).
However, the closest logical choice based on the steps involved in distribution is:
**Option 2:**
\(3x(x) + 3x(-4) + -1(x) + -1(-4)\)
While it does not give the final simplified expression, it accurately represents the steps of distributing each term.
If you have specific instructions regarding acceptable answers, please let me know!
The correct expansion using the distributive property gives us:
1. \(3x \cdot x = 3x^2\)
2. \(3x \cdot (-4) = -12x\)
3. \(-1 \cdot x = -x\)
4. \(-1 \cdot (-4) = 4\)
Combining all the terms yields:
\[
3x^2 - 12x - x + 4 = 3x^2 - 13x + 4
\]
Now, looking at the four options you provided:
1. \(3x^2 + 6x + 4\)
2. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)
3. \(3x(-1) + 3x(3x) + x(-4) + x(x)\)
4. \(3x^2 - 5x + 4\)
None of the options match the correct result of \(3x^2 - 13x + 4\).
However, the closest logical choice based on the steps involved in distribution is:
**Option 2:**
\(3x(x) + 3x(-4) + -1(x) + -1(-4)\)
While it does not give the final simplified expression, it accurately represents the steps of distributing each term.
If you have specific instructions regarding acceptable answers, please let me know!
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