A student expanded the expression −6(4x−213)

Question

. 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.

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

No, the student should have multiplied 4x
and −213
by 6
.

Answer 1

The correct response to the question about the student's expansion of the expression \( -6(4x - 213) \) is:

No, the student should have multiplied 4x and −213 by −6.

To expand the expression correctly, you need to apply the distributive property, which means multiplying each term inside the parentheses by \(-6\).

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

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

So, the correct expanded form is:
\(-24x + 1278\)

If the student's work did not yield this result, then they made a mistake in the expansion process.