Use the order of operations to simplify 2[(7−3)^2+(18−16)^2]+13

To simplify the expression \( 2[(7-3)^2 + (18-16)^2] + 13 \), we will follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right, commonly referred to as PEMDAS).

Let's break it down step by step:

1. **Calculate the parentheses**:
- \( 7 - 3 = 4 \)
- \( 18 - 16 = 2 \)

Now our expression looks like this:
\[
2[(4)^2 + (2)^2] + 13
\]

2. **Calculate the exponents**:
- \( 4^2 = 16 \)
- \( 2^2 = 4 \)

Now the expression simplifies to:
\[
2[16 + 4] + 13
\]

3. **Calculate inside the brackets**:
- \( 16 + 4 = 20 \)

Now we have:
\[
2[20] + 13
\]

4. **Perform the multiplication**:
- \( 2 \times 20 = 40 \)

Now the expression is:
\[
40 + 13
\]

5. **Finally, perform the addition**:
- \( 40 + 13 = 53 \)

Therefore, the simplified expression is \( \boxed{53} \).