Let's break down the mathematical expression step-by-step to evaluate:
Given expression:
[tex]\[
-(3-2)^2 + 2^2 \cdot 4
\][/tex]
1. First Step:
Calculate inside the parenthesis:
[tex]\[
3 - 2 = 1
\][/tex]
2. Second Step:
Evaluate the square of the result from the first step:
[tex]\[
(1)^2 = 1
\][/tex]
3. Third Step:
Apply the negative sign to the squared result:
[tex]\[
-(1) = -1
\][/tex]
4. Fourth Step:
Evaluate the exponentiation [tex]\(2^2\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
5. Fifth Step:
Multiply the squared result by 4:
[tex]\[
4 \cdot 4 = 16
\][/tex]
6. Sixth Step:
Combine the results from third and fifth steps:
[tex]\[
-1 + 16 = 15
\][/tex]
So, the final result of the given expression is:
[tex]\[
15
\][/tex]
