Question

Justine tried to evaluate an expression. Here is her work:
10–4+2(4)2
=
Step 110–4+82
=
Step 210–4+64
=
Step 36+64
=
Step 470
Is Justine's work correct? Is Justine's work correct?
No, Justine made a mistake going from the given expression to Step 1. Justine should have squared 4 before multiplying. The order of operations says to evaluate exponents before you multiply.
No, Justine made a mistake going from Step 2 to Step 3. Justine should have added before she subtracted. The order of operations says to add before you subtract.
Yes, Justine's work is correct.

Answer 1

Let's review Justine's calculations step by step while following the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

The expression is:
\[ 10 - 4 + 2(4)^2 \]

1. Calculate the exponent \( (4)^2 \):
\[ 4^2 = 16 \]

2. Substitute this back into the expression:
\[ 10 - 4 + 2(16) \]

3. Perform the multiplication:
\[ 2 \times 16 = 32 \]
Now the expression is:
\[ 10 - 4 + 32 \]

4. Now we perform the addition and subtraction from left to right:
- First, \( 10 - 4 = 6 \)
- Then, \( 6 + 32 = 38 \)

So the final answer is 38.

Justine's first step was incorrect because she did not calculate \( (4)^2 \) before multiplying. Hence, the correct response is:
**No, Justine made a mistake going from the given expression to Step 1. Justine should have squared 4 before multiplying. The order of operations says to evaluate exponents before you multiply.**