To solve $14 - (-3)^2 - 4 \cdot (-2)^2$, we need to follow the order of operations (PEMDAS/BODMAS):

1. Parentheses/Brackets
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

Let's go through each step carefully:

Step 1: Simplify the exponents

• $(-3)^2 = 9$ because $(-3) \cdot (-3) = 9$.
• $(-2)^2 = 4$ because $(-2) \cdot (-2) = 4$.

So, the expression becomes: $14 - 9 - 4 \cdot 4$

Step 2: Perform the multiplication

• $4 \cdot 4 = 16$.

Now the expression is: $14 - 9 - 16$

Step 3: Perform the subtraction

1. $14 - 9 = 5$.
2. $5 - 16 = -11$.

Final Answer:

$14 - (-3)^2 - 4 \cdot (-2)^2 = -11$

Would you like more details on any part of the calculation?

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Here are 5 related questions to explore further:

1. How does the order of operations affect the outcome of expressions?
2. What happens if we change the signs in similar expressions?
3. How do negative exponents influence the calculations?
4. Why does squaring a negative number result in a positive value?
5. How does the distributive property apply to expressions with multiple terms?

Tip: Always evaluate exponents before moving to multiplication or subtraction to avoid errors in calculations.