Absolutely, let's evaluate the expression step-by-step:
Given Expression:
[tex]\[ 4 \cdot 2 - \left((-1)^3 - 3\right)^2 \][/tex]
### Step 1: Evaluate the innermost exponentiation and subtraction
First, we need to calculate the value of [tex]\((-1)^3\)[/tex]:
[tex]\[ (-1)^3 = -1 \][/tex]
Next, subtract 3 from this result:
[tex]\[ -1 - 3 = -4 \][/tex]
So, the expression now looks like this:
[tex]\[ 4 \cdot 2 - (-4)^2 \][/tex]
### Step 2: Evaluate the square of the result from Step 1
Next, square [tex]\(-4\)[/tex]:
[tex]\[ (-4)^2 = 16 \][/tex]
So our expression now is:
[tex]\[ 4 \cdot 2 - 16 \][/tex]
### Step 3: Multiply and Subtract
Next, perform the multiplication:
[tex]\[ 4 \cdot 2 = 8 \][/tex]
Finally, subtract [tex]\(16\)[/tex] from [tex]\(8\)[/tex]:
[tex]\[ 8 - 16 = -8 \][/tex]
### Final Result
The evaluated result of the given expression is:
[tex]\[ \boxed{-8} \][/tex]
