A student was simplifying the expression below and showed these steps.

In which step did the student make a mistake? ... explain the mistake made!

The expression: 4(−3𝑥 + 2) + 14𝑥 + 2

step 1 distribute: -12x + 8 + 14x + 2

step 2 combine like terms: 2x + 8

answer is  2x + 8

The student made a mistake in **Step 1** during the distribution process. Here's a detailed explanation of the mistake:

### The Original Expression:
\[ 4(-3x + 2) + 14x + 2 \]

### Step 1: Distribute \(4\) to \(-3x\) and \(2\)
The correct distribution should be:
\[ 4 \times -3x = -12x \]
\[ 4 \times 2 = 8 \]

So, after correctly distributing, the expression should be:
\[ -12x + 8 + 14x + 2 \]

**However, the mistake occurred here:** The expression after distribution was written correctly, but the mistake in combining like terms suggests that the issue might be due to an error in the next step.

### Step 2: Combine Like Terms
The student combined like terms incorrectly:
\[ -12x + 14x = 2x \]
\[ 8 + 2 = 10 \]

The correct combination should give:
\[ 2x + 10 \]

### Final Answer:
The correct simplified expression should be:
\[ 2x + 10 \]

So, **Step 2** is where the mistake is evident, where they incorrectly combined the constants \(8\) and \(2\), but identified the wrong error.

### Corrected Steps:
1. **Distribution:**
   \[ 4(-3x + 2) + 14x + 2 \]
   \[ -12x + 8 + 14x + 2 \]

2. **Combine Like Terms:**
   \[ (-12x + 14x) + (8 + 2) \]
   \[ 2x + 10 \]

**Answer:** The correct simplified expression is \( 2x + 10 \).

### Summary:
- The error occurred in Step 2 when the student combined the constants incorrectly.

Do you want more details or have any other questions?

### Related Questions:
1. How do you distribute a number across a binomial expression?
2. What are "like terms" and how do you combine them?
3. Can you explain the process of simplifying algebraic expressions?
4. What are some common mistakes made during the distribution process?
5. How do you check your work when simplifying expressions?

### Tip:
Always double-check your combination of like terms to ensure all terms are properly added or subtracted, especially the constants.

Learn how to identify mistakes when simplifying algebraic expressions step-by-step. This example covers distribution, combining like terms, and provides a detailed explanation of where a common mistake occurs. Suitable for students in Grades 7-9.

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