Question

Dwayne tried to evaluate an expression. Here is his work:
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 \(539\).