A student expanded the expression%C2%A0 −6(4x−213) . Is the student's work correct? If not, what was their mistake? (1 point) Responses No, the student should have added%C2%A0−6 %C2%A0to%C2%A04x %C2%A0and%C2%A0−213 . No, the student should have added%C2%A0negative 6%C2%A0to%C2%A04 x%C2%A0and%C2%A0negative 2 over 13. No, the student should have multiplied%C2%A04x %C2%A0and%C2%A0−213 %C2%A0by%C2%A0−6 . No, the student should have multiplied%C2%A04 x%C2%A0and%C2%A0negative 2 over 13%C2%A0by%C2%A0negative 6. Yes, the student's work is correct. Yes, the student's work is correct. No, the student should have multiplied%C2%A04x %C2%A0and%C2%A0−213 %C2%A0by%C2%A06 .

Question

A student expanded the expression%C2%A0 −6(4x−213)  . Is the student's work correct? If not, what was their mistake?    (1 point) Responses  No, the student should have added%C2%A0−6 %C2%A0to%C2%A04x %C2%A0and%C2%A0−213 . No, the student should have added%C2%A0negative 6%C2%A0to%C2%A04 x%C2%A0and%C2%A0negative 2 over 13.  No, the student should have multiplied%C2%A04x %C2%A0and%C2%A0−213 %C2%A0by%C2%A0−6 . No, the student should have multiplied%C2%A04 x%C2%A0and%C2%A0negative 2 over 13%C2%A0by%C2%A0negative 6.  Yes, the student's work is correct. Yes, the student's work is correct.  No, the student should have multiplied%C2%A04x %C2%A0and%C2%A0−213 %C2%A0by%C2%A06 .

GPT-4o mini · Answer

To expand the expression $-6(4x - 213)$, the student should apply the distributive property, which involves multiplying $-6$ by each term inside the parentheses. Let's correctly expand the expression step by step: 1. Multiply $-6$ by $4x$: $$ -6 \times 4x = -24x $$ 2. Multiply $-6$ by $-213$: $$ -6 \times -213 = 1278 $$ Now, combine these results: $$ -6(4x - 213) = -24x + 1278 $$ Now we can analyze the student's potential mistakes based on the options given: - No, the student should have added $-6$ to $4x$ and $-213$. (Incorrect) - No, the student should have added negative 6 to $4x$ and negative $2/13$. (Incorrect) - No, the student should have multiplied $4x$ and $-213$ by $-6$. (Incorrect) - No, the student should have multiplied $4x$ and negative $2/13$ by negative 6. (Incorrect) - Yes, the student's work is correct. (Correct option if student expanded correctly) - No, the student should have multiplied $4x$ and $-213$ by $6$. (Incorrect) If we assume the options are referring to wrong steps, it seems that the key mistakes revolve around misunderstanding the distribution process or mixing terms incorrectly. Based on this breakdown, if the student's work involves correctly applying the distributive property, then "Yes, the student's work is correct" is the appropriate response.