Question

A student expanded the expression −6(4x−213)
. Is the student's work correct? If not, what was their mistake?



(1 point)
Responses

No, the student should have multiplied 4x
and −213
by −6
.
No, the student should have multiplied 4 x and negative 2 over 13 by negative 6.

No, the student should have added −6
to 4x
and −213
.
No, the student should have added negative 6 to 4 x and negative 2 over 13.

No, the student should have multiplied 4x
and −213
by 6
.
No, the student should have multiplied 4 x and negative 2 over 13 by 6.

Yes, the student's work is correct.
Yes, the student's work is correct.
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Answer 1

To determine if the student's work expanding the expression \( -6(4x - 213) \) is correct, we need to perform the expansion ourselves.

When we expand \( -6(4x - 213) \), we distribute \( -6 \) to both terms inside the parentheses:

1. Multiply \( -6 \) by \( 4x \):
\[
-6 \cdot 4x = -24x
\]

2. Multiply \( -6 \) by \( -213 \):
\[
-6 \cdot -213 = 1278
\]

Putting it all together, the expanded expression is:
\[
-24x + 1278
\]

Now, we will evaluate the response options:

1. **No, the student should have multiplied 4x and −213 by −6.**
2. **No, the student should have multiplied 4x and negative 2 over 13 by negative 6.**
3. **No, the student should have added −6 to 4x and −213.**
4. **No, the student should have added negative 6 to 4 x and negative 2 over 13.**
5. **No, the student should have multiplied 4x and −213 by 6.**
6. **No, the student should have multiplied 4 x and negative 2 over 13 by 6.**
7. **Yes, the student's work is correct.**

The correct reasoning is that the student should have multiplied both \( 4x \) and \( -213 \) by \( -6 \), so they should not deviate from that process.

The correct option is:
**No, the student should have multiplied 4x and −213 by −6.**