To evaluate the expression [tex]\(-5 \cdot (-2) + \left(2 - 2^2\right)^2\)[/tex], let's break it down into smaller steps and solve each part individually.
1. Evaluate the first part:
[tex]\[
-5 \cdot (-2)
\][/tex]
Multiplying these two numbers gives:
[tex]\[
-5 \cdot (-2) = 10
\][/tex]
2. Evaluate the expression inside the parentheses:
[tex]\[
2 - 2^2
\][/tex]
First, compute [tex]\(2^2\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
Next, perform the subtraction:
[tex]\[
2 - 4 = -2
\][/tex]
3. Square the result of the expression inside the parentheses:
[tex]\[
\left(-2\right)^2
\][/tex]
Squaring [tex]\(-2\)[/tex] gives:
[tex]\[
(-2)^2 = 4
\][/tex]
4. Sum the results of both parts:
[tex]\[
10 + 4
\][/tex]
Adding these two numbers together gives:
[tex]\[
10 + 4 = 14
\][/tex]
So, the final result of the expression [tex]\(-5 \cdot (-2) + \left(2 - 2^2\right)^2\)[/tex] is [tex]\(\boxed{14}\)[/tex].
