Let's evaluate the expression step by step to check Justine's work:
The expression is \( 10 - 4 + 2(4)^2 \).
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First, calculate \( (4)^2 \): \[ (4)^2 = 16 \] So now our expression is: \[ 10 - 4 + 2 \cdot 16 \]
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Next, calculate \( 2 \cdot 16 \): \[ 2 \cdot 16 = 32 \] Now the expression is: \[ 10 - 4 + 32 \]
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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:
- She began with \( 10 - 4 + 2(4)^2 \), which is correct.
- She mistakenly moved to \( 10 - 4 + 8^2 \) instead of \( 10 - 4 + 32 \) after calculating \( 2(4)^2 \).
- 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 \( 38 \).