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

Question

. Is the student's work correct? If not, what was their mistake?

(1 point)
Responses

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

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.

No, the student should have added −6
to 4x
and −213
.

Answer 1

To determine if the student's work is correct when expanding the expression −6(4x − 213), we need to follow the distributive property, which states that we need to multiply each term inside the parentheses by −6.

Let's break it down:

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

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

Putting it all together gives us: \(-24x + 1278\)

Now, looking at the options provided:

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

So the student's work is not correct, and the correct response would be that they needed to multiply both terms by −6.