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
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?

Answer 1

Let's evaluate the expression step by step to check Justine's work:

The expression is \( 10 - 4 + 2(4)^2 \).

1. First, calculate \( (4)^2 \):
\[
(4)^2 = 16
\]
So now our expression is:
\[
10 - 4 + 2 \cdot 16
\]

2. Next, calculate \( 2 \cdot 16 \):
\[
2 \cdot 16 = 32
\]
Now the expression is:
\[
10 - 4 + 32
\]

3. Now we perform the calculations from left to right:
- First, calculate \( 10 - 4 \):
\[
10 - 4 = 6
\]
- Now replace it in the expression:
\[
6 + 32
\]
- Finally, calculate \( 6 + 32 \):
\[
6 + 32 = 38
\]

Thus, the correct value of the expression \( 10 - 4 + 2(4)^2 \) is \( 38 \).

Now let's analyze Justine's steps:

1. She began with \( 10 - 4 + 2(4)^2 \), which is correct.
2. She mistakenly moved to \( 10 - 4 + 8^2 \) instead of \( 10 - 4 + 32 \) after calculating \( 2(4)^2 \).
3. She continued on with incorrect calculations leading to a final incorrect answer of \( 70 \).

So, Justine's work is incorrect, and the correct answer should be \( 38 \).