Question

1. a student incorrectly used the distributive property and wrote $3(2x + 4)=6x + 4$. which of the following is the best explanation to help the student correct their error? they have added $2x$ and $3$ rather than multiplying them. they have multiplied $2x$ and $3$ rather than adding them. they have forgotten to multiply the second part of the sum, $4$, by the number outside the parentheses, $3$. they have have multiplied the wrong term in the sum by $3$. they should multiply $4$, instead of $2x$, by $3$.

Explanation:

The distributive property states that \( a(b + c)=ab + ac \). For \( 3(2x + 4) \), we need to multiply 3 by both \( 2x \) and 4. The student got \( 6x+4 \), which means they multiplied 3 by \( 2x \) (correctly getting \( 6x \)) but forgot to multiply 3 by 4 (which should be \( 12 \), not \( 4 \)). So the error is forgetting to multiply the second part (4) by 3.

• Option A: The student did multiply \( 2x \) and 3 (got \( 6x \)), so A is wrong.
• Option B: The distributive property uses multiplication, not addition, so B is wrong.
• Option D: The student did multiply \( 2x \) by 3 (correct), and the error is not multiplying 4, not multiplying the wrong term, so D is wrong.

Answer:

C. They have forgotten to multiply the second part of the sum, 4, by the number outside the parentheses, 3.