Dwayne tried to evaluate an expression. Here is his work:

Question

3+542–(5–2)2
=
3+542–32 Step 1
=
3+5[16–9] Step 2
=
3+57 Step 3
=
3+35 Step 4
=
38 Step 5
Is Dwayne's work correct?

Answer 1

Let's carefully evaluate the expression \(3 + 542 - (5 - 2)2\) step by step to see if Dwayne's work is correct.

1. Original Expression: \[ 3 + 542 - (5 - 2)2 \]

2. Calculate the parentheses: \[ 5 - 2 = 3 \] So, now the expression becomes: \[ 3 + 542 - 3 \cdot 2 \]

3. Multiply: \[ 3 \cdot 2 = 6 \] Now, the expression is: \[ 3 + 542 - 6 \]

4. Calculate \(542 - 6\): \[ 542 - 6 = 536 \] So now we have: \[ 3 + 536 \]

5. Add: \[ 3 + 536 = 539 \]

So the final result of the expression \(3 + 542 - (5 - 2)2\) is \(539\).

Now, looking at Dwayne's work:

• In Step 1, he correctly simplifies \(3 + 542 - (5 - 2)2\) to \(3 + 542 - 32\).
• However, in Step 2, he incorrectly simplifies \(32\) as \(32 = 16 - 9\), which is incorrect. \(32 = 32\).
• The errors continue from there, and he ends up with a final answer of \(38\), which is not correct.

Hence, Dwayne's work is not correct. The correct answer to the expression is \(539\).