Question

problem 3
$(5 + 3)^2 - 4 \times 2$
student work:
$5 + 3^2 - 4 \times 2$
$5 + 9 - 8$
$6$
what went wrong?

Explanation:

Step1: Identify order of operations

First compute inside parentheses: $(5+3)=8$

Step2: Calculate the exponent

$8^2 = 64$

Step3: Perform multiplication

$4 \times 2 = 8$

Step4: Subtract to find the correct value

$64 - 8 = 56$

Step5: Analyze student error

The student incorrectly evaluated $5+3^2$ instead of $(5+3)^2$, ignoring the parentheses and squaring only 3 instead of the sum of 5 and 3.

Answer:

The student failed to follow the order of operations (PEMDAS/BODMAS) by not calculating the sum inside the parentheses first. Instead of squaring the result of $5+3$, they only squared 3. The correct answer to the expression is 56.