The expression in the image is:

$-\left(1 - (-2)^2\right)^2 + 3 \cdot (-5)$

Step-by-step solution:

1. Evaluate the innermost part first: $(-2)^2 = 4$

2. Substitute back into the expression: $-(1 - 4)^2 + 3 \cdot (-5)$

3. Simplify the subtraction: $1 - 4 = -3$ Now the expression becomes: $-(-3)^2 + 3 \cdot (-5)$

4. Square $-3$: $(-3)^2 = 9$ So the expression is now: $-9 + 3 \cdot (-5)$

5. Simplify the multiplication: $3 \cdot (-5) = -15$ Now the expression is: $-9 - 15$

6. Final subtraction: $-9 - 15 = -24$

Final Answer:

$-24$

Would you like further details or have any questions?

Here are 5 related questions to further explore this topic:

1. How does the order of operations (PEMDAS) apply to this problem?
2. What would happen if the negative signs were removed from the terms?
3. How would the result change if we replaced $-2$ with another number?
4. What is the significance of squaring a negative number in algebra?
5. How can we verify the solution using a calculator?

Tip: Always simplify inside parentheses and handle exponents before dealing with multiplication and subtraction for complex expressions.