We need to simplify the expression in problem 1: $4\{100 - [3^2 - 2(10 - 6)]\}$.

1. Problem Description

We need to simplify the expression in problem 1: $4\{100 - [3^2 - 2(10 - 6)]\}$.

2. Solution Steps

First, we simplify the innermost parentheses:

$10 - 6 = 4$

So the expression becomes:

$4\{100 - [3^2 - 2(4)]\}$

Next, we evaluate the square and the multiplication inside the brackets:

$3^2 = 9$

$2(4) = 8$

The expression becomes:

$4\{100 - [9 - 8]\}$

Simplify the expression inside the brackets:

$9 - 8 = 1$

So the expression becomes:

$4\{100 - 1\}$

Subtract within the curly braces:

$100 - 1 = 99$

So the expression becomes:

$4\{99\}$

Finally, we multiply:

$4 \times 99 = 396$

3. Final Answer

396