Answer :
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].
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].