Math Problem Statement
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(β3π₯ + 2) + 14π₯ + 2
step 1 distribute: -12x + 8 + 14x + 2
step 2 combine like terms: 2x + 8
answer is 2x + 8
Solution
The student made a mistake in Step 1 during the distribution process. Here's a detailed explanation of the mistake:
The Original Expression:
Step 1: Distribute to and
The correct distribution should be:
So, after correctly distributing, the expression should be:
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:
The correct combination should give:
Final Answer:
The correct simplified expression should be:
So, Step 2 is where the mistake is evident, where they incorrectly combined the constants and , but identified the wrong error.
Corrected Steps:
-
Distribution:
-
Combine Like Terms:
Answer: The correct simplified expression is .
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:
- How do you distribute a number across a binomial expression?
- What are "like terms" and how do you combine them?
- Can you explain the process of simplifying algebraic expressions?
- What are some common mistakes made during the distribution process?
- 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.
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Math Problem Analysis
Mathematical Concepts
Algebra
Distribution
Combining Like Terms
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9
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