Jacki evaluated the expression below.

Question

2 cubed (3 minus 1) + 4 (8 minus 12) = 2 cubed (2) + 4 (4) = 8 (2) + 16 = 16 + 16 = 32.

What was Jacki’s error?
Jacki should have simplified the exponent first.
Jacki should have multiplied 4 and 8 first.
Jacki did not subtract 12 from 8 correctly.
Jacki should not have multiplied 8 and 2.

Answer 1

Let's analyze Jacki's evaluation step-by-step to identify her error.

Jacki starts with the expression:

\[ 2^3 (3 - 1) + 4 (8 - 12) \]

1. She evaluates \( (3 - 1) \) and \( (8 - 12) \):

   • \( (3 - 1) = 2 \)
   • \( (8 - 12) = -4 \)

2. Now substituting these values back into the expression, we get: \[ 2^3 (2) + 4 (-4) \]

3. Next, she calculates \( 2^3 \):

   • \( 2^3 = 8 \)

4. Substituting this value, we have: \[ 8 (2) + 4 (-4) \]

5. Perform the multiplications:

   • \( 8 \times 2 = 16 \)
   • \( 4 \times -4 = -16 \)

6. Now substituting these multiplications into the expression gives: \[ 16 - 16 = 0 \]

Jacki mistakenly calculated both the calculations from the subtraction operations as well as the final result.

The error in Jacki’s initial evaluation stemmed from incorrectly calculating \( 4 (8 - 12) \).

The correct evaluation should yield: \[ 2^3 (3 - 1) + 4 (8 - 12) = 16 + (-16) = 0 \]

So, the correct answer is: Jacki did not subtract 12 from 8 correctly.