Let's analyze the given expression and find the error in the student's calculation step-by-step.
Original Expression:
[tex]\[ 2^3(2-4) + 5(3-8) \][/tex]
Step-by-step simplification:
1. Simplify inside the parentheses:
[tex]\[ 2^3(-2) + 5(-5) \][/tex]
2. Evaluate the exponent:
[tex]\[ 8 \cdot (-2) + 5 \cdot (-5) \][/tex]
3. Multiply:
[tex]\[ -16 + (-25) \][/tex]
4. Add the results:
[tex]\[ -16 - 25 = -41 \][/tex]
The correct result is [tex]\(-41\)[/tex].
Student's Calculation:
[tex]\[ \begin{array}{c}
2^3(2-4)+5(3-8) \\
2^3(-2)+5(5) \\
8(-2)+25 \\
-16+25 \\
9
\end{array}
\][/tex]
Let's inspect the student's calculation:
1. Starting Point:
[tex]\[ 2^3(2-4)+5(3-8) \][/tex]
This step is correct.
2. Simplified parentheses:
[tex]\[ 2^3(-2)+5(5) \][/tex]
Here lies an error. Instead of correctly evaluating [tex]\(3-8\)[/tex] to get [tex]\(-5\)[/tex], the student evaluated it incorrectly as [tex]\(5\)[/tex].
3. Apply exponent:
[tex]\[ 8(-2)+25 \][/tex]
This step follows from the incorrect simplification in the previous step.
4. Multiplication:
[tex]\[ -16+25 \][/tex]
This step is consistent with the student's mistake in step 2.
5. Addition:
[tex]\[ 9 \][/tex]
This step also follows from previous incorrect values.
Hence, the error in the student's calculation occurred during the subtraction inside the parentheses. The student incorrectly calculated [tex]\(3-8\)[/tex] as [tex]\(5\)[/tex] instead of [tex]\(-5\)[/tex].
Conclusion:
The error is that the student did not subtract 3 and 8 correctly.
