Let's solve the expression step by step:

The given expression is:

\[
(5 \times 5)^2 - \left( (5 - 1)(5 + 1) \right)^2
\]

### Step 1: Simplify each part separately.
1. **First part:**
\[
(5 \times 5)^2 = (25)^2 = 625
\]

2. **Second part:**
\[
(5 - 1)(5 + 1) = 4 \times 6 = 24
\]
\[
(24)^2 = 576
\]

### Step 2: Substitute the simplified values into the expression:
\[
625 - 576
\]

### Step 3: Subtract:
\[
625 - 576 = 49
\]

Thus, the final result is:

\[
\boxed{49}
\]

Would you like further clarification on any of these steps or a deeper explanation?

Here are 5 related questions to explore:
1. What is the difference between squaring a sum and a difference?
2. How do you expand the binomial formula \((a+b)^2\)?
3. How does squaring affect negative numbers in expressions?
4. What are perfect squares and how are they useful in solving equations?
5. How does factoring help in simplifying complex algebraic expressions?

**Tip:** Always remember the order of operations (PEMDAS) when simplifying expressions: parentheses, exponents, multiplication/division, and addition/subtraction.

Learn how to simplify the expression (5*5)² - ((5-1)(5+1))² using algebraic methods, including the difference of squares theorem. Follow a step-by-step guide to solve this problem, which is suitable for students in Grades 7-9.

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