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

Answer 1

To determine if the student's work is correct, let's expand the expression \( -6(4x - 213) \).

Using the distributive property:

\[ -6(4x) + (-6)(-213) \]

Calculating each term:

1. \( -6 \cdot 4x = -24x \)
2. \( -6 \cdot -213 = 1278 \) (because multiplying two negatives results in a positive)

So the expanded expression is:

\[ -24x + 1278 \]

Now, examining the possible answers:

• "No, the student should have multiplied 4x and −213 by −6." (This statement is correct in essence; they should have multiplied.)
• "No, the student should have multiplied 4 x and negative 2 over 13 by negative 6." This is not correct because the original problem has different terms.
• "Yes, the student's work is correct." This is incorrect as their work was not shown.
• "No, the student should have added −6 to 4x and −213." This is incorrect; the operation required is multiplication.
• "No, the student should have added negative 6 to 4 x and negative 2 over 13." This is also incorrect for similar reasons.
• "No, the student should have multiplied 4x and −213 by 6." This is incorrect, as they should multiply by -6, not 6.

The correct response is closest to: "No, the student should have multiplied 4x and −213 by −6." This indicates the correct process of expansion via multiplication.